C-Paracompactness and $C_2$-paracompactness

Abstract

A topological space X is called C -paracompact if there exist a paracompact space Y and a bijective function f : X −→ Y such that the restriction f |A : A −→ f (A) is a homeomorphism for each compact subspace A ⊆ X . A topological space X is called C2 -paracompact if there exist a Hausdorff paracompact space Y and a bijective function f : X −→ Y such that the restriction f |A : A −→ f (A) is a homeomorphism for each compact subspace A ⊆ X . We investigate these two properties and produce some examples to illustrate the relationship between them and C -normality, minimal Hausdorff, and other properties.