We present a concise survey of old and new results concerning cardinal functions on
topological groups and then establish various relations between the classes of σ-compact, ℵ …

A (Hausdorff) topological group is said to have a 𝔊-base if it admits a base of
neighbourhoods of the unit, ${U_ {α}: α∈ ℕ^{ℕ}} $, such that $ U_ {α}⊂ U_ {β} $ whenever …

In this paper we investigate the topological structure of free topological universal algebras
with given continuous signature. We establish some properties of compact subsets of free …

In this paper the free topological vector space V (X) over a Tychonoff space X is defined and
studied. It is proved that V (X) is ak ω-space if and only if X is ak ω-space. If X is infinite, then …

Characterizations of a metrizable space X such that every A,(X) is a k-space Page 1 Topology
and its Applications 49 (1993) 75-94 North-Holland 7s Characterizations of a metrizable space …

Abstract Let F (X) and A (X) be respectively the free topological group and the free abelian
topological group on a Tychonoff space X. For all natural number n we denote by Fn (X)(An …

Based on the notions of T. Banakh's strict Pytkeev networks and AV Arhangel'skiı̌'s sensor
families, strict Pytkeev networks with sensors are introduced in this paper. A family P of …

A family of closed subsets of a topological space $ X $ is called a (strict) $ Cld $-fan in $ X $
if this family is (strictly) compact-finite but not locally finite in $ X $. Applications of (strict) …

Let $ F (X) $ and $ A (X) $ be respectively the free topological group and the free Abelian
topological group on a Tychonoff space $ X $. For every natural number $ n $ we denote by …

The theory of generalized metrizable spaces is an important topic of general topology. This
paper is a survey of research methods and achievements on generalized metrizable …