Funcoids and Reloids

Authors: Victor Porton

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.

Comments: 53 pages

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Submission history

[v1] 16 Mar 2010
[v2] 17 Mar 2010
[v3] 26 Mar 2010
[v4] 29 Mar 2010
[v5] 21 Apr 2010
[v6] 13 Jun 2010
[v7] 21 Sep 2010
[v8] 25 Sep 2010
[v9] 28 Oct 2010
[vA] 30 Oct 2010
[vB] 2 Nov 2010
[vC] 4 Nov 2010
[vD] 2 Dec 2010
[vE] 3 Dec 2010
[vF] 29 Jul 2011
[vG] 2 Aug 2011
[vH] 10 Aug 2011
[vI] 19 Aug 2011

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