Displaying similar documents to “Relatively realcompact sets and nearly pseudocompact spaces”

Some results and problems about weakly pseudocompact spaces

Oleg Okunev, Angel Tamariz-Mascarúa (2000)

Commentationes Mathematicae Universitatis Carolinae

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A space X is if X is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with χ ( x , X ) > ω for every x ∈ X ; (2) every locally bounded space is truly weakly pseudocompact; (3) for ω < κ < α , the κ -Lindelöfication of a discrete space of cardinality α is weakly pseudocompact if κ = κ ω .

Closed embeddings into complements of Σ -products

Aleksander V. Arhangel&amp;#039;skii, Miroslav Hušek (2008)

Commentationes Mathematicae Universitatis Carolinae

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In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a Σ -subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin...