Previous months:
2010 - 1003(2)
2012 - 1205(2) - 1211(1)
2013 - 1302(2) - 1305(1)
Any replacements are listed further down
[7] viXra:1305.0066 [pdf] submitted on 2013-05-11 14:40:41
Authors: I. Ramabhadrasarma, J. Madhusudanan Rao, S. Sambasiva Rao
Comments: 4 Pages. To Appear in Global Journal of Mathematical Science: Theory and Practical [GJMS] ISSS NO. 0974-3200. We presented paper in the NCAMEI 2013 organized by Kakatiya University, Warangal, Andhrapradesh, India.
The purpose of this note is to show that (a) the concepts of metric and D*-metric are topologically identical, and (b) propose a slight generalization
of a fixed point theorem in a metric space and exploit (a) above to derive an improved version of a known fixed point theorem in D-metric spaces.
Category: Topology
[6] viXra:1302.0039 [pdf] submitted on 2013-02-06 20:33:41
Authors: Nasir Germain
Comments: 4 Pages.
my new spin on mathematics
Category: Topology
[5] viXra:1302.0011 [pdf] submitted on 2013-02-02 07:56:10
Authors: Jaivir Baweja
Comments: 2 Pages.
Let $M$ be a smooth manifold. In this paper we review the definition of a germ
and show that since it is an equivalence relation, the concept is only locally defined.
Category: Topology
[4] viXra:1205.0082 [pdf] submitted on 2012-05-20 11:09:22
Authors: Terry Allen, Daniel Branscombe, Jim Bury
Comments: 50 Pages.
The musical staff notates Pitch Value Vectors whereas tablature, using fret numbers on string lines, denotes Position Value Vectors, forming a commuting algebra of Hilbert Spaces. In 2001 I demonstrated that music is semi-algebraic (Allen and Goudessenue).
Pitch Value Space is undefined without a connection to pitch, and when connected to pitch by a barycenter, becomes defined and complete.
A defined musical system must have at least 2 functions, the chromatic f(x) and the harmonic function g(x) that form a composite function with at most 1 common center (Music Multicentricity Theorem). Thus tonality is defined by the line of tonal projection that marries pitch to position to make a musical tone.
Since musical systems must have a tone generator (instrument or device) the music topos must be the triple composite function f⋅g⋅h where f(x) is a + b + c = 0 and g(x) > 0 is a scale center and h(x) > 0 an instrument center. A music cipher as defined here as an affine projection that marries R:Z pitch to position to compose a note [tone point as an orthonormal pair (position value, pitch value)]. The harmonic message is embedded in a musical system by the cipher which defines tonality, so that (harmony, tonality) is another orthonormal pair.
A cipher can also make a new note from one already known in a system.
The only algebraic operation in a musical topos is vector additions to a single barycenter according to a difference function defined by the complete lattice of the musical system, and according to the Boolean Arithmetic Operator of the Music Cipher which forms the geometry of tone value spaces by its prime ideals. The cipher model is therefore simple and natural compared to current music topology requiring two centers and several algebraic operators.
Music is composed by the finite union of notes and open intervals defined by the composite functions of the fundamental, the key, and the intonation algorithm.
Tonality, the sum total of every function, relation, and element in a musical system, is the same as the algebraic-logic interface (numeric key) of the pitch-position intonation algorithm that is precisely the triangle of cipher vectors formed between one logic and at least two algebraic sub lattices. The cipher vector defined by a complete musical lattice is also the same as the arithmetic tone values closure operator that defines tonal geometry. Specifically, the cipher is precisely the projection between the logic sub lattice and at least two algebraic sub lattices in the musical system, where the sub lattices all share the fundamental as 1 common center.
Therefore the cipher is equivalent to a point, a line, a triangle, and a sphere, reflections resulting from line-point duality in geometry. Without a common center for the R: Z cipher the musical clock is undefined: Euler's donut is dead.
The new model is a clock: the fundamental is the hour hand, the instrument position is the minute hand, and scale position is the third hand. Tonality, like time on the clock, is a vector as a composite of three functions with 1 fundamental in common. Therefore, tonality has at least two functions but at most one center.
Category: Topology
[3] viXra:1205.0081 [pdf] submitted on 2012-05-20 16:05:13
Authors: Tuomas Korppi
Comments: 39 Pages.
A homology theory based on both near-standard and non-near-standard
microsimplices is constructed. Its basic properties, including
Eilenberg-Steenrod axioms for homology and continuity with respect to resolutions
of spaces, are proved.
Category: Topology
[2] viXra:1003.0267 [pdf] submitted on 30 Mar 2010
Authors: Victor Porton
Comments: 4 pages
Considered convergence and limit for funcoids (a generalization of proximity spaces).
I also have defined (generalized) limit for arbitrary (not necessarily continuous)
functions under certain conditions.
This article is a part of my Algebraic General Topology research.
Category: Topology
[1] viXra:1003.0192 [pdf] submitted on 16 Mar 2010
Authors: Victor Porton
Comments: 32 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity space, the concept of reloid is cleared from superfluous details (generalized)
concept of uniform space. Also funcoids and reloids are generalizations of binary relations
whose domains and ranges are filters (instead of sets).
That funcoids and reloids are common generalizations of both (proximity, pretopology,
uniform) spaces and of (multivalued) functions, makes this theory smart for analyzing
properties (e.g. continuousness) of functions on spaces. Also funcoids and reloids can be
considered as a generalization of (oriented) graphs, this provides us with a common
generalization of analysis and discrete mathematics.
Category: Topology
[18] viXra:1211.0165 [pdf] replaced on 2013-01-26 19:02:37
Authors: Cheng Tianren
Comments: 27 Pages.
In this paper ,we introduce weak fixed point and schauder conjecture.we put forward three inference in this paper. The first two are about weak fixed point’s properties.in which, we use analysis methods and operator theory. (functional analisis methods mainly).the last one is a problem about schauder conjecture，which elaborate schauder’s applictionin in analysis and topology . in this article,we use some tools, with the help of these tools,we start to discuss these problems.
Category: Topology
[17] viXra:1003.0192 [pdf] replaced on 19 Aug 2011
Authors: Victor Porton
Comments: 53 pages
It is a part of my Algebraic General Topology research.
In this article, I introduce the concepts of funcoids, which generalize proximity spaces
and reloids, which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept of
uniformity. Also funcoids generalize pretopologies and preclosures. Also funcoids and reloids
are generalizations of binary relations whose domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs, this
provides us with a common generalization of analysis and discrete mathematics. The concept of continuity is defined by an algebraic formula (instead of old messy epsilondelta notation) for arbitrarymorphisms (including funcoids and reloids) of a partially ordered category. In one formula are generalized continuity, proximity continuity, and uniform continuity.
Category: Topology
[16] viXra:1003.0192 [pdf] replaced on 10 Aug 2011
Authors: Victor Porton
Comments: 52 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[15] viXra:1003.0192 [pdf] replaced on 2 Aug 2011
Authors: Victor Porton
Comments: 52 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[14] viXra:1003.0192 [pdf] replaced on 29 Jul 2011
Authors: Victor Porton
Comments: 52 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[13] viXra:1003.0192 [pdf] replaced on 3 Dec 2010
Authors: Victor Porton
Comments: 46 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[12] viXra:1003.0192 [pdf] replaced on 2 Dec 2010
Authors: Victor Porton
Comments: 45 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[11] viXra:1003.0192 [pdf] replaced on 4 Nov 2010
Authors: Victor Porton
Comments: 44 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[10] viXra:1003.0192 [pdf] replaced on 2 Nov 2010
Authors: Victor Porton
Comments: 44 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[9] viXra:1003.0192 [pdf] replaced on 30 Oct 2010
Authors: Victor Porton
Comments: 43 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[8] viXra:1003.0192 [pdf] replaced on 28 Oct 2010
Authors: Victor Porton
Comments: 42 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[7] viXra:1003.0192 [pdf] replaced on 25 Sep 2010
Authors: Victor Porton
Comments: 42 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[6] viXra:1003.0192 [pdf] replaced on 21 Sep 2010
Authors: Victor Porton
Comments: 41 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[5] viXra:1003.0192 [pdf] replaced on 13 Jun 2010
Authors: Victor Porton
Comments: 39 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[4] viXra:1003.0192 [pdf] replaced on 21 Apr 2010
Authors: Victor Porton
Comments: 39 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially
ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[3] viXra:1003.0192 [pdf] replaced on 29 Mar 2010
Authors: Victor Porton
Comments: 38 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a
partially ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[2] viXra:1003.0192 [pdf] replaced on 26 Mar 2010
Authors: Victor Porton
Comments: 37 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept
of uniformity. Also funcoids and reloids are generalizations of binary relations whose
domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a
partially ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology
[1] viXra:1003.0192 [pdf] replaced on 17 Mar 2010
Authors: Victor Porton
Comments: 33 pages
It is a part of my Algebraic General Topology research.
In this article I introduce the concepts of funcoids which generalize proximity spaces
and reloids which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity space, the concept of reloid is cleared from superfluous details (generalized)
concept of uniform space. Also funcoids and reloids are generalizations of binary relations
whose domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs,
this provides us with a common generalization of analysis and discrete mathematics.
The concept of continuity is defined by an algebraic formula (instead of old messy
epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a
partially ordered category. In one formula are generalized continuity, proximity continuity,
and uniform continuity.
Category: Topology