Abstract
A topological space X is called C-regular if there exists a one-to-one function f from X onto a regular space Y such that the restriction f vertical bar K : K -> f (K) is a homeomorphism for each compact subspace K subset of X. We discuss this property and illustrate the relationships between C-regularity and some other properties such as submetrizability, local compactness, L-regularity, C-normality, epinormality, epiregularity, sigma-compactness and semiregularity.