A real topological vector space is said to have the Krein–Milman property if every bounded,
closed, convex subset has an extreme point. In the case of every bounded, closed, convex …

The stereographic projection is constructed in topological modules. Let A be an additively
symmetric closed subset of a topological R-module M such that 0∈ int (A). If there exists a …

Chaotic and pathological phenomena in topological modules are studied in this manuscript.
In particular, constructions of noncontinuous linear functionals are provided for a wide …

The extremal structure of zero-neighbourhoods of a topological module is analyzed
reaching unexpected conclusions when the module topology is not Hausdorff. These results …

This article is devoted to investigations of a structure and homomorphisms of microbundles.
Microbundles are generalizations of manifolds. For manifolds it was studied when their …

This survey paper is devoted to the algebraic theory of rings of continuous functions. The
author considers the relationship between topological spaces and the corresponding rings …

This survey presents results on specification of topological spaces by various algebraic
structures of continuous functions. Results are presented on specification of E-compact …

Let K be a class of associative topological algebras that is closed under subalgebras with
the induced topology, direct products, quotients, and semidirect topological products with …

The structure of an $ alpha_ {(beta, beta)} $-topological ring is richer in comparison with the
structure of an $ alpha_ {(beta, beta)} $-topological group. The theory of $ alpha_ {(beta …

A study is presented of the relationship between the topological and uniformity properties of
a group G and the spaces ℐ (G), ℒ (G) of all nonempty closed subsets and closed …