A generalization of the Vitali covering theorem

D. Sarkhel

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Commentationes Mathematicae Universitatis Carolinae

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J. Keesling has shown that for connected spaces $X$ the natural inclusion $e : X \to β X$ of $X$ in its Stone-Čech compactification is a shape equivalence if and only if $X$ is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.