$C$-Normal Topological Property

Samirah Alzahrani, Lutfi Kalantan

A topological space $X$ is called $C$-normal if there exist a normal space $\Upsilon$ and a bijective function $f\colon X\to\Upsilon$ such that the restriction $f\upharpoonright C\colon C\to f(C)$ is a homeomorphism for each compact subspace $C\subseteq X$. We investigate this property and present some examples to illustrate the relationships between $C$-normality and other weaker kinds of normality.