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July 30, 2019 / porton

Monograph “Algebraic General Topology. Volume 1” sent for publication

I’ve sent the final version of the first edition of my research monograph Algebraic General Topology. Volume 1 (download here) to Russian publisher INFRA-M and signed the publication contract. They are going to publish my book electronically. They also asked to send them a Russian translation of my book to publish both in print and electronically.

The monograph contains the biggest discovery in general topology since 1937 (when filters were discovered).

Here is the abstract of the book:

In this work I introduce and study in details the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces, and generalizations thereof. The concept of funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details (generalized) concept of uniformity.

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 calculus and discrete mathematics.

The concept of continuity is defined by an algebraic formula (instead of old messy epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially ordered category. In one formula continuity, proximity continuity, and uniform continuity are generalized.

Also I define connectedness for funcoids and reloids.

Then I consider generalizations of funcoids: pointfree funcoids and generalization of pointfree funcoids: staroids and multifuncoids. Also I define several kinds of products of funcoids and other morphisms.

Before going to topology, this book studies properties of co-brouwerian lattices and filters.

Here is the fascinating story of my life while it was discovered.

Now the discovery is finally sent for an official publication after many years.

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