Results about C-κ-normality and C-mild normality

Abstract

A topological space X is C-κ-normal (C-mildly normal ) if there exist a κ-normal (mildly normal) 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 present new results about those two topological properties and use a discrete extension space to solve open problems regarding C2-paracompactness and α-normality