Some problems and lines of investigation in general topology
Aleksander V. Arhangel'skii (1988)
Commentationes Mathematicae Universitatis Carolinae
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Displaying similar documents to “Selections and suborderability”
Some problems and lines of investigation in general topology
On a problem of Katětov
Wage, M. L.
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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...
Addition theorems and -spaces
Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is proved that if a regular space is the union of a finite family of metrizable subspaces then is a -space in the sense of E. van Douwen. It follows that if a regular space of countable extent is the union of a finite collection of metrizable subspaces then is Lindelöf. The proofs are based on a principal result of this paper: every space with a point-countable base is a -space. Some other new results on the properties of spaces which are unions of a finite collection of...
The number of metrizable spaces
Richard Hodel (1983)
Fundamenta Mathematicae
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On clopen sets in Cartesian products
Raushan Z. Buzyakova (2001)
Commentationes Mathematicae Universitatis Carolinae
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The results concern clopen sets in products of topological spaces. It is shown that a clopen subset of the product of two separable metrizable (or locally compact) spaces is not always a union of clopen boxes. It is also proved that any clopen subset of the product of two spaces, one of which is compact, can always be represented as a union of clopen boxes.