| Title:
|
Rectangular covers of products missing diagonals (English) |
| Author:
|
Yajima, Yukinobu |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
147-153 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a characterization of a paracompact $\Sigma$-space to have a $G_\delta$-diagonal in terms of three rectangular covers of $X^2\setminus\Delta$. Moreover, we show that a local property and a global property of a space $X$ are given by the orthocompactness of $(X\times\beta X)\setminus\Delta$. (English) |
| Keyword:
|
$\Sigma$-space |
| Keyword:
|
$G_\delta$-diagonal |
| Keyword:
|
$\sigma$-closure-preserving |
| Keyword:
|
$\sigma$-cushioned |
| Keyword:
|
rectangular cover |
| Keyword:
|
\newline orthocompact |
| Keyword:
|
metacompact |
| Keyword:
|
Fréchet space |
| MSC:
|
54B10 |
| MSC:
|
54D20 |
| MSC:
|
54E18 |
| idZBL:
|
Zbl 0804.54010 |
| idMR:
|
MR1292590 |
| . |
| Date available:
|
2009-01-08T18:09:29Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118648 |
| . |
| Reference:
|
[1] Arhangel'skiĭ A.V., Kombarov A.P.: On $\nabla$-normal spaces.Topology and Appl. 35 (1990), 121-126. MR 1058792 |
| Reference:
|
[2] Chaber J., Čoban M., Nagami N.: On monotonic generalizations of Moore spaces, Čech-complete spaces, and $p$-spaces.Fund. Math. 83 (1974), 107-119. MR 0343244 |
| Reference:
|
[3] Gruenhage G.: Generalized metric spaces.Handbook of Set-theoretic Topology (K. Kunen and J.E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 423-501. Zbl 0794.54034, MR 0776629 |
| Reference:
|
[4] Gruenhage G., Pelant J.: Analytic spaces and paracompactness of $X^2\setminus\Delta$.Topology and Appl. 28 (1988), 11-15. Zbl 0636.54025, MR 0927277 |
| Reference:
|
[5] Junnila H.J.K.: Metacompactness, paracompactness and interior-preserving open covers.Trans. Amer. Math. Soc. 249 (1979), 373-385. Zbl 0404.54017, MR 0525679 |
| Reference:
|
[6] Junnila H.J.K.: On submetacompactness.Topology Proc. 3 (1978), 375-405. MR 0540503 |
| Reference:
|
[7] Kombarov A.P.: On rectangular covers of $X^2\setminus\Delta$.Comment. Math. Univ. Carolinae 30 (1989), 81-83. MR 0995704 |
| Reference:
|
[8] Nagami K.: $\Sigma$-spaces.Fund. Math. 65 (1969), 169-192. Zbl 0181.50701, MR 0257963 |
| Reference:
|
[9] Yajima Y.: A characterization of submetacompactness in terms of products.Proc. Amer. Math. Soc. 112 (1991), 291-296. Zbl 0722.54017, MR 1054165 |
| Reference:
|
[10] Yajima Y.: Subspaces of squares; $X^2\setminus\Delta$ and others.Abstracts of Short Conference of Uniform Mathematics and its Applications, Bern, 1991. |
| . |
