Some topological properties of C-normality

Abstract

A topological space X is C-normal if there exists a bijective function f : X → Y , for some normal space Y , such that the restriction f ↾C : C → f(C) is a homeomorphism for each compact C ⊂ X. The purpose of this work is to extend the known classes of C-normal spaces and clarify the behavior of C-normality under several usual topological operations; in particular, it is proved that C-normality is not preserved under closed subspaces, unions, continuous and closed images, and inverse images under perfect functions. These results are used to answer some questions raised in [1], [2] and [6].