Star-covering properties: Generalized Ψ-spaces, countability conditions, reflection

Regular Generalized Star Star closed sets in Bitopological Spaces

The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces. Keywords—τ1τ2-regular closed sets; τ1τ2-regular open sets; τ1τ2-regular generalized closed sets; τ1τ2-regular generalized star closed sets; τ1τ2-regular generalized star star closed sets.

Selections on Ψ - spaces

We show that if A is an uncountable AD (almost disjoint) family of subsets of ω then the space Ψ(A) does not admit a continuous selection; moreover, if A is maximal then Ψ(A) does not even admit a continuous selection on pairs, answering thus questions of T. Nogura.

Generalized Calderón Conditions and Regular Orbit Spaces

The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L(A) requires the existence of a square-integrable function whose Plancherel transform satisfies Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable funct...

Covering Spaces

Some Algebraic Properties of Universal and Regular Covering Spaces

Let X̃ be a connected space, X be a space, let p : X̃ −→ X be a continuous map and let (X̃, p) be a covering space of X . In the first section we give some preliminaries from covering spaces and their automorphism groups. In the second section we derive some algebraic properties of both universal and regular covering spaces (X̃, p) of X and also their automorphism groups A(X̃, p). Keywords—covering ...