$C$-Paracompactness and $C_2$-paracompactness

Authors: MAHA MOHAMMED, LUTFI KALANTAN, HALA ALZUMI

Abstract: A topological space $X$ is called $C$-paracompact if there exist a paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f|_{A}:A\longrightarrow f(A)$ is a homeomorphism for each compact subspace $A\subseteq X$. A topological space $X$ is called $C_2$-paracompact if there exist a Hausdorff paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f|_{A}:A\longrightarrow f(A)$ is a homeomorphism for each compact subspace $A\subseteq X$. We investigate these two properties and produce some examples to illustrate the relationship between them and $C$-normality, minimal Hausdorff, and other properties.

Keywords: Normal, paracompact, $C$-paracompact, $C_2$-paracompact, $C$-normal, epinormal, mildly normal, minimal Hausdorff, Fréchet, Urysohn

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