Previous months: - 1003(2)
Any replacements are listed further down
[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
[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