In this paper analogous to [1], we introduce a new class of sets called ωθ˜-µ-open in generalized topological spaces which lies strictly between the θ˜µ-open and ω-µ-open sets. We prove that collection forms topology. Finally, several characterizations properties have been given.

Let X be a h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. It is shown that the universal minimal space M(G) of the topological group G = Homeo(X), is the space of maximal chains on X introduced in [Usp00]. If X is metrizable then clearly X is homeomorphic to the Cantor set and the result was already known (see [GW03]). However ma...

In this paper, another generalized class of τ⋆ called mildly Igω-closed sets is introduced and the notion of mildly Ig-ω-open sets in ideal topological spaces is introduced and studied. The relationships of mildly Igω-closed sets with various other sets are investigated.

we introduce some new concepts of topological spaces which say α − separable topologicalspace and o-topological group, α − first axiom, α − second axiom, and we find some relations betweenthem with some applications in normed spaces.

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

Topological groups whose underlying spaces are basically disconnected, F-, or F′-spaces but not P-spaces considered. It is proved, in particular, that the existence of a Lindelöf disconnected topological group which P-space equivalent to Boolean countable pseudocharacter, free and Abelian zero-dimensional non-P-spaces never F′-spaces, F′-group selective ultrafilters on ω.

Let Homeo(Ω) be the group of all homeomorphisms of a Cantor set Ω. We study topological properties of Homeo(Ω) and its subsets with respect to the uniform (τ) and weak (τ w) topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in τ and τ w are found. 0 Introduction The present paper is a continuation of our...

Let Homeo(Ω) be the group of all homeomorphisms of a Cantor set Ω. We study topological properties of Homeo(Ω) and its subsets with respect to the uniform (τ) and weak (τ w) topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in τ and τ w are found. 0 Introduction The present paper is a continuation of our...

We introduce a notion of productivity (summability) of sequences in a topological group G, parametrized by a given function f : N → ω+1. The extreme case when f is the function taking constant value ω is closely related to the TAP property, the weaker version of the wellknown property NSS. We prove that TAP property coincides with NSS in locally compact groups, ω-bounded abelian groups and coun...

We prove that if a paratopological group G is a continuous image of an arbitrary product of regular Lindelöf Σ-spaces, then it is R-factorizable and has countable cellularity. If in addition, G is regular, then it is totally ω-narrow and satisfies celω(G) ≤ ω, and the Hewitt–Nachbin completion of G is again an R-factorizable paratopological group.