$C$-Paracompactness and $C_2$-paracompactness

Authors : Maha MOHAMMED, LUTFI KALANTAN, HALA ALZUMI

Pages : 9-20

View : 11 | Download : 8

Publication Date : 0000-00-00

Article Type : Research Paper

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 $f|_{A}:A\longrightarrow finsert ignore into journalissuearticles values(A);$ 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 $f|_{A}:A\longrightarrow finsert ignore into journalissuearticles values(A);$ 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