Some Properties of Spaces Similar to Čech-Complete Property

Dušan Milovančević

Mathematica Moravica, Tome 4 (2000) no. 1.

Résumé

In this paper we study some notions related to the remainder $X^{\ast}=\beta X\backslash\beta(X)$ which are similar to the Čech-complete property. A topological space $X$ is $P(\omega P)$-complete if $X$ is a Tychonoff space and remainder $X^{\ast}=\beta X\backslash\beta(X)$ is a $P(\omega P)$-set in $\beta X$. The set $A\subset X$ is an $L$-set if $A\cap cl_{X}(F)=\emptyset$ for each Lindelöf subset $F$ contained in $X\backslash A$. Recall that a space $X$ is said to be $L$-complete if $X$ is a Tychonoff space and the remainder $X^{\ast}=\beta X\backslash\beta(X)$ is and $L$-set in $\beta X$.

Détail

Mots-clés : Extension spaces, remainders, completions