[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]**
*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