$L$-paracompactness and $L_2$-paracompactness

Abstract

A  topological space $X$ is called $L$-paracompact if there exist a paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f\upharpoonright_{A}:A\longrightarrow f(A)$ is a homeomorphism for each Lindelö}f subspace $A\subseteq X$. A  topological space $X$ is called $L_2$-paracompact if there exist a Hausdorff paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f\upharpoonright_{A}:A\longrightarrow f(A)$ is a homeomorphism for each Lindelöf subspace $A\subseteq X$. We investigate these two properties.

Keywords

• Lindelöf,paracompact,countably normal,$C$-paracompact,$C_2$-paracompact,$L$-paracompact,$L_2$-paracompact,$L$-normal,$CP$,$C_2P$

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