# Ordered Semicategory Actions

## General Topology as Ordered Semigroup Actions

**Several** new axiomatic systems as general and as important as group theory. It starts from generalizing proximity spaces and topologies and later moves to ordered semigroup actions and ordered semicategory actions that encompass *all* kinds of spaces that are met in general topology: from locales and frames to metric spaces.

## The particular topics

*every*function.

*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 semicategory 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.

**Purchasing this book, you support carbon accounting and DeSci (decentralized science).**

### Victor Porton

Your instructor is Victor Porton, the person who discovered *ordered
semigroup actions* (and wrote 500 pages about them), a theory as
general as group theory but unknown before. Victor Porton is a
programming languages polyglot, author of multitudinous softwares
and programming libraries, blockchain expert and winner of
multitudinous blockchain hackathons, author of several books,
a philosopher.

Victor Porton studied math in a university 4.5 years, but didn't receive a degree because of discrimination.

This book describes a generalization of general topology, done in an algebraic way instead of non-algebraic mess of traditional general topology.

Ordered semigroup actions and ordered semicategory actions were discovered by Victor Porton in 2019. At the same time it was discovered that every kind of spaces met in general topology, from metric spaces to locales and frames are fully characterizable by an element of an ordered semigroup action (or a morphism of an ordered semicategory action). Thus, general topology is nothing other as the algebra of ordered semicategory actions.

Almost, I discovered the general notion of space for purposes of general topology. “Geometric spaces” (like Euclidean spaces) don’t (yet) fit into this notion.

I want prize money, because I need funds for further research and publication.

I think, completely reducing all general topology (from metric spaces to locales and frames) to an algebraic concept (ordered semicategory actions) is quite worth Abel Prize.