On Some Properties of the Class of Charming Spaces

Abstract

We study the properties of class of charming spaces. It is proved that if $X$ is the preimage of a metrizable locally Lindel\"{o}f $p$-space(respectively, locally s-space)under a perfect mapping, then every remainder $bX\setminus X$ of $X$ in a compactification $bX$ is 1-strong charming(respectively, charming). Some corollaries realted to this statement are presented. It is shown that let $X$ be a metrizable space, if $X$ is a locally Lindel\"{o}f $p$-space(respectively, locally s-space), then for any compactification $bX$ of $X$ the remainder $bX\setminus X$ of $X$ is 1-strong charming (respectively, charming). It is also proved that let $X$ be a nowhere locally compact metrizable space, then $X$ is a locally s-space (respectively, locally Lindel\"{o}f $p$-space) if and only if for any (for some) compactification $bX$ of $X$, the remainder $bX\setminus X$ of $X$ is charming (respectively, 1-strong charming). Some related propositions are proved within this section. In addition, some properties about s-space are investigated.