Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1804-54
Keywords
Normal, paracompact, $C$-paracompact, $C_2$-paracompact, $C$-normal, epinormal, mildly normal, minimal Hausdorff, Fréchet, Urysohn
First Page
9
Last Page
20
Recommended Citation
MOHAMMED, M, KALANTAN, L, & ALZUMI, H (2019). $C$-Paracompactness and $C_2$-paracompactness. Turkish Journal of Mathematics 43 (1): 9-20. https://doi.org/10.3906/mat-1804-54
