C-Tychonoff and L-Tychonoff Topological Spaces (European Journal of Pure and Applied Mathematics, 2018)
A topological space X is called C-Tychonoff if there exist a one-to-one function f from X onto a Tychonoff space Y such that f restriction K from K onto f(K) is a homeomorphism for each compact subspace K of X. We discuss this property and illustrate the relationships between C-Tychonoffness and some other properties like submetrizability, local compactness, L-Tychononess, C-normality, C-regularity, epinormality, sigma-compactness, pseudocompactness and zero-dimensional.
Keywords: Tychonoff; C-Tychonoff; C-normal; C-regular; epinormal; submetrizable; L-Tychonoff.