CC-Tychonoffness, CCT3 and CC-Almost Regularity

Following the notion of so-called C-normality - a weaker version of normality in topological spaces as proposed by A. V. Arhangel’skii, further weaker version called CC-normality is studied by Kalantan et al [14]. In this paper, we investigate various type of properties such as CC-complete regularity, CC-almost complete regularity, CC-regularity, CC-almost regularity, CCT3 and CC-Tychonoffness. A space (X, T ) is called a CC-completely regular (resp. CC-almost completely regular, CC-regular, CC-almost regular, CCT3, CC-Tychonoff) space if there exist a completely regular (resp. almost completely regular, regular, almost regular, T3, Tychonoff) space Y and a bijective function f : X → Y such that the restriction function f|A : A → f(A) is a homeomorphism for each countably compact subspace A ⊆ X. We study these properties and present some examples to illustrate the relationships among them with other forms of topological properties.