| Title:
|
On clopen sets in Cartesian products (English) |
| Author:
|
Buzyakova, Raushan Z. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
357-362 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
clopen set |
| Keyword:
|
clopen box |
| Keyword:
|
Cartesian product of spaces |
| MSC:
|
54B10 |
| MSC:
|
54B15 |
| MSC:
|
54D20 |
| MSC:
|
54H05 |
| MSC:
|
55M10 |
| idZBL:
|
Zbl 1053.54016 |
| idMR:
|
MR1832154 |
| . |
| Date available:
|
2009-01-08T19:10:41Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119250 |
| . |
| Reference:
|
[ARH] Arhangel'skii A.: private communications.1999. |
| Reference:
|
[BAU] Bauer A.: private communications.2000. |
| Reference:
|
[ENG] Engelking R.: General Topology.Sigma Series in Pure Mathematics 6, Heldermann, Berlin, revised ed., 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[KUN] Kunen K.: private communications.2000. |
| Reference:
|
[STE] Stephenson R.M.: Product space and the Stone-Weierstrass theorem.General Topology Appl. 3 (1973), 77-79. MR 0315669 |
| Reference:
|
[SHO] 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. |
| Reference:
|
[SaS] Steprans J., Shostak A.: Restricted compactness properties and their preservation under products.Topology Appl. 11 (2000), 213-229. Zbl 0962.54020, MR 1733805 |
| . |
