| Title:
|
On minimal-$\alpha$-spaces (English) |
| Author:
|
Lo Faro, G. |
| Author:
|
Nordo, G. |
| Author:
|
Porter, J. R. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
727-740 |
| . |
| Category:
|
math |
| . |
| Summary:
|
An $\alpha$-space is a topological space in which the topology is generated by the family of all $\alpha$-sets (see [N]). In this paper, minimal-$\alpha\Cal P$-spaces (where $\Cal P$ denotes several separation axioms) are investigated. Some new characterizations of $\alpha$-spaces are also obtained. (English) |
| Keyword:
|
$\alpha$-space |
| Keyword:
|
$\alpha T_i$-space |
| Keyword:
|
minimal-$\alpha T_i$ space |
| Keyword:
|
$T_2$-closed space |
| Keyword:
|
minimal-$T_2$ space |
| Keyword:
|
$\psi$-space |
| MSC:
|
54A05 |
| MSC:
|
54A10 |
| MSC:
|
54D25 |
| MSC:
|
54D80 |
| idZBL:
|
Zbl 1097.54003 |
| idMR:
|
MR2062889 |
| . |
| Date available:
|
2009-01-08T19:32:33Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119427 |
| . |
| Reference:
|
[D] Dontchev J.: Survey on pre-open sets.preprint, 1999. |
| Reference:
|
[E] Engelking R.: General Topology.Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[L] Larson R.: Minimal $T_0$-spaces and minimal $T_D$-spaces.Pacific J. Math. 31 (1969), 451-458. MR 0251688 |
| Reference:
|
[Le] Levine N.: Semi-open sets and semi-continuity in topological spaces.Amer. Math. Monthly 70 (1963), 36-41. Zbl 0113.16304, MR 0166752 |
| Reference:
|
[Lo] Lo Faro G.: Su alcune proprietà degli insieme $\alpha$-aperti.Atti Sem. Mat. Fis. Univ. Modena XXIX (1980), 242-252 (in Italian). |
| Reference:
|
[N] Njåstad O.: On some classes of nearly open sets.Pacific J. Math. 15 3 (1965), 961-970. MR 0195040 |
| Reference:
|
[PW] Porter J.R., Woods R.G.: Extensions and Absolutes of Hausdorff Spaces.Springer, New York, 1988. Zbl 0652.54016, MR 0918341 |
| Reference:
|
[T] Tall F.D.: The density topology.Pacific J. Math. 62 (1976), 275-284. Zbl 0305.54039, MR 0419709 |
| . |
