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