Overview
I define space as an element of an ordered semigroup action, that is a semigroup action conforming to a partial order. Topological spaces, uniform spaces, proximity spaces, (directed) graphs, metric spaces, etc. all are spaces. It can be further generalized to ordered precategory actions (that I call interspaces). I build basic general topology (continuity, limit, openness, closedness, hausdorffness, compactness, etc.) in an arbitrary space. Now general topology is an algebraic theory.For example, my generalized continuous function are: continuous function for topological spaces, proximally continuous functions for proximity spaces, uniformly continuous functions for uniform spaces, contractions for metric spaces, discretely continuous functions for (directed) graphs.Was a spell laid onto Earth mathematicians not to find the most important structure in general topology until 2019?
- | Author: Victor Lvovich Porton
- | Publisher: Independently Published
- | Publication Date: November 23, 2019
- | Number of Pages: 63 pages
- | Language: English
- | Binding: Paperback
- | ISBN-10: 1710826711
- | ISBN-13: 9781710826715
