On clopen sets in Cartesian products

Raushan Z. Buzyakova

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 2, page 357-362
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Buzyakova, Raushan Z.. "On clopen sets in Cartesian products." Commentationes Mathematicae Universitatis Carolinae 42.2 (2001): 357-362. <http://eudml.org/doc/248819>.

@article{Buzyakova2001,
abstract = {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.},
author = {Buzyakova, Raushan Z.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {clopen set; clopen box; Cartesian product of spaces; clopen set; clopen box; Cartesian product},
language = {eng},
number = {2},
pages = {357-362},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On clopen sets in Cartesian products},
url = {http://eudml.org/doc/248819},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Buzyakova, Raushan Z.
TI - On clopen sets in Cartesian products
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 2
SP - 357
EP - 362
AB - 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.
LA - eng
KW - clopen set; clopen box; Cartesian product of spaces; clopen set; clopen box; Cartesian product
UR - http://eudml.org/doc/248819
ER -

References

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  1. Arhangel'skii A., private communications, 1999. 
  2. Bauer A., private communications, 2000. 
  3. Engelking R., General Topology, Sigma Series in Pure Mathematics 6, Heldermann, Berlin, revised ed., 1989. Zbl0684.54001MR1039321
  4. Kunen K., private communications, 2000. 
  5. Stephenson R.M., Product space and the Stone-Weierstrass theorem, General Topology Appl. 3 (1973), 77-79. (1973) MR0315669
  6. Shostak A., On a class of spaces containing all bicompacts and all connected spaces, in General Topology and its Relations to Modern Analysis and Algebra, Proceeding of the Forth Prague Topological Symposium, Vol. B, 1976. 
  7. Steprans J., Shostak A., Restricted compactness properties and their preservation under products, Topology Appl. 11 (2000), 213-229. (2000) Zbl0962.54020MR1733805

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