We consider the following problem: For which Tychonoff topological spaces X do the free
topological group F (X) and the free abelian topological group A (X) admit a nontrivial (ie not …

The topological group version of the celebrated Banach-Mazur problem asks wether every
infinite topological group has a non-trivial separable quotient group. It is known that compact …

In this paper, some generalizations of the topological group namely 𝛼-topological group, 𝑏-
topological group, and 𝛽-topological group were defined with illustrative examples. In …

Let E be any metrizable nuclear locally convex space and E^ the Pontryagin dual group of E.
Then the topological group E^ has the tubby torus (that is, the countably infinite product of …