Results on C2-paracompactness

Hala Alzumi, Lutfi Kalantan, Maha Mohammed Saeed

Abstract

A C-paracompact is a topological space X associated with a paracompact space Y and a bijective function f : X −→ Y satisfying that f A: A −→ f(A) is a homeomorphism for each compact subspace A ⊆ X. Furthermore, X is called C2-paracompact if Y is T2 paracompact. In this article, we discuss the above concepts and answer the problem of Arhangel’ski ̆i. Moreover, we prove that the sigma product Σ(0) can not be condensed onto a T2 paracompact space.

Keywords

normal, paracompact, sigma product, $C$-paracompact, $C_2$-paracompact, $C$-normal, sigma product, open invariant, Alexandroff duplicate.

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