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For a cardinal $α$ , we say that a subset $B$ of a space $X$ is $C_{α}$ -compact in $X$ if for every continuous function $f X \to ℝ^{α}$ , $f [B]$ is a compact subset of $ℝ^{α}$ . If $B$ is a $C$ -compact subset of a space $X$ , then $ρ (B, X)$ denotes the degree of $C_{α}$ -compactness of $B$ in $X$ . A space $X$ is called $α$ -pseudocompact if $X$ is $C_{α}$ -compact into itself. For each cardinal $α$ , we give an example of an $α$ -pseudocompact space $X$ such that $X \times X$ is not pseudocompact: this answers a question posed by T. Retta in “Some cardinal generalizations of pseudocompactness”...

Spaces with zero set bases

Michael L. Wage (1977)

Commentationes Mathematicae Universitatis Carolinae

Subgroups of $ℝ$ -factorizable groups

Constancio Hernández, Mihail G. Tkachenko (1998)

Commentationes Mathematicae Universitatis Carolinae

The properties of $ℝ$ -factorizable groups and their subgroups are studied. We show that a locally compact group $G$ is $ℝ$ -factorizable if and only if $G$ is $σ$ -compact. It is proved that a subgroup $H$ of an $ℝ$ -factorizable group $G$ is $ℝ$ -factorizable if and only if $H$ is $z$ -embedded in $G$ . Therefore, a subgroup of an $ℝ$ -factorizable group need not be $ℝ$ -factorizable, and we present a method for constructing non- $ℝ$ -factorizable dense subgroups of a special class of $ℝ$ -factorizable groups. Finally, we construct a closed...

Sur les fonctions vectorielles approximativement continues

Zbigniew Grande, Maria Topolewska (1982)

Časopis pro pěstování matematiky

Sur les sélecteurs des multifonctions

Milan Matejdes (1987)

Mathematica Slovaca

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