Algebraic objects generated by topological structure

Abstract

The survey examines the properties of the Tikhonov space X that depend on the topological properties of the function space C(X) with pointwise topology and of the free topological group F(X). It covers the part of the theory of topological groups dealing with topological invariants and topological classification of topological groups. Continuous images of topological groups are considered in the context of studying the actions of topological groups on spaces.