Compact covers and function spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

On function spaces of Corson-compact spaces

We apply elementary substructures to characterize the space Cp(X) for Corsoncompact spaces. As a result, we prove that a compact space X is Corson-compact, if Cp(X) can be represented as a continuous image of a closed subspace of (Lτ ) × Z, where Z is compact and Lτ denotes the canonical Lindelöf space of cardinality τ with one non-isolated point. This answers a question of Archangelskij [2].

Limits in Function Spaces and Compact Groups ∗

If B is an infinite subset of ω and X is a topological group, let CX B be the set of all x ∈ X such that 〈xn : n ∈ B〉 converges to 1. If F is a filter of infinite sets, let DX F = ⋃{CX B : B ∈ F}. The CX B and DX F are subgroups of X when X is abelian. In the circle group T, it is known that CX B always has measure 0. We show that there is a filter F such that DT F has measure 0 but is not cont...

Fuzzifying Strongly Compact Spaces and Fuzzifying Locally Strongly Compact Spaces

In this paper, some characterizations of fuzzifying strong compactness are given, including characterizations in terms of nets and pre -subbases. Several characterizations of locally strong compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

Compact and strictly singular operators on certain function spaces