Algebraic General Topology. Book 3: Algebra

Algebraic General Topology. Book 3: Algebra

Size: 387.0 KB

Available Licenses

 US$ 9.99 Download to own (unlimited viewing, no burn)

Description

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, connectedness, 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?