# On clopen sets in Cartesian products

Commentationes Mathematicae Universitatis Carolinae (2001)

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

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topBuzyakova, 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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- Stephenson R.M., Product space and the Stone-Weierstrass theorem, General Topology Appl. 3 (1973), 77-79. (1973) MR0315669
- 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.
- 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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