On a problem of Katětov
Wage, M. L.
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Displaying similar documents to “On the subsets of non locally compact points of ultracomplete spaces”
On a problem of Katětov
Closed embeddings into complements of -products
Aleksander V. Arhangel'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 -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...
Čech-completeness and ultracompleteness in “nice spaces”
Miguel López de Luna, Vladimir Vladimirovich Tkachuk (2002)
Commentationes Mathematicae Universitatis Carolinae
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We prove that if is a union of subspaces of pointwise countable type then the space is of pointwise countable type. If is a countable union of ultracomplete spaces, the space is ultracomplete. We give, under CH, an example of a Čech-complete, countably compact and non-ultracomplete space, giving thus a partial answer to a question asked in [BY2].