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Strong remote points

Sergei Logunov (2002)

Commentationes Mathematicae Universitatis Carolinae

Remote points constructed so far are actually strong remote. But we construct remote points of another type.

Strong shape of the Stone-Čech compactification

Sibe Mardešić (1992)

Commentationes Mathematicae Universitatis Carolinae

J. Keesling has shown that for connected spaces X the natural inclusion e : X 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.

Sum theorems for Ohio completeness

D. Basile, J. van Mill, G. J. Ridderbos (2008)

Colloquium Mathematicae

We present several sum theorems for Ohio completeness. We prove that Ohio completeness is preserved by taking σ-locally finite closed sums and also by taking point-finite open sums. We provide counterexamples to show that Ohio completeness is preserved neither by taking locally countable closed sums nor by taking countable open sums.

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