Previous months: - 1002(1) - 1003(2)
[3] 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.
[2] 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.
[1] viXra:1002.0005 [pdf] submitted on 3 Feb 2010
Authors: Victor Porton
Comments: 57 pages
Studied in details properties of filters on lattices, filters on posets, and certain generalizations thereof. Also done some more general lattice theory research. Posed several open problems. Detailed study of filters is required for my ongoing research which will be published as "Algebraic General Topology" series.
[9] 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.
[8] 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.
[7] 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.
[6] 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.
[5] 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.
[4] viXra:1002.0005 [pdf] replaced on 7 Jun 2010
Authors: Victor Porton
Comments: 62 pages
Studied in details properties of filters on lattices, filters on posets, and certain generalizations thereof. Also done some more general lattice theory research. Posed several open problems. Detailed study of filters is required for my ongoing research which will be published as "Algebraic General Topology" series.
[3] viXra:1002.0005 [pdf] replaced on 21 Apr 2010
Authors: Victor Porton
Comments: 61 pages
Studied in details properties of filters on lattices, filters on posets, and certain generalizations thereof. Also done some more general lattice theory research. Posed several open problems. Detailed study of filters is required for my ongoing research which will be published as "Algebraic General Topology" series.
[2] viXra:1002.0005 [pdf] replaced on 16 Mar 2010
Authors: Victor Porton
Comments: 61 pages
Studied in details properties of filters on lattices, filters on posets, and certain generalizations thereof. Also done some more general lattice theory research. Posed several open problems. Detailed study of filters is required for my ongoing research which will be published as "Algebraic General Topology" series.
[1] viXra:1002.0005 [pdf] replaced on 26 Feb 2010
Authors: Victor Porton
Comments: 59 pages
Studied in details properties of filters on lattices, filters on posets, and certain generalizations thereof. Also done some more general lattice theory research. Posed several open problems. Detailed study of filters is required for my ongoing research which will be published as "Algebraic General Topology" series.