| Title:
|
Almost closed sets and topologies they determine (English) |
| Author:
|
Tkachuk, V. V. |
| Author:
|
Yaschenko, I. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
395-405 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that every countably compact AP-space is Fréchet-Urysohn. It is also established that if $X$ is a paracompact space and $C_p(X)$ is AP, then $X$ is a Hurewicz space. We show that every scattered space is WAP and give an example of a hereditarily WAP-space which is not an AP-space. (English) |
| Keyword:
|
AP-space |
| Keyword:
|
WAP-space |
| Keyword:
|
scattered space |
| Keyword:
|
countably compact space |
| Keyword:
|
function space |
| Keyword:
|
discretely generated space |
| MSC:
|
54A25 |
| MSC:
|
54D20 |
| MSC:
|
54D55 |
| MSC:
|
54G12 |
| idZBL:
|
Zbl 1053.54004 |
| idMR:
|
MR1832158 |
| . |
| Date available:
|
2009-01-08T19:11:08Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119254 |
| . |
| Reference:
|
[ASh] Amirdzhanov G.P., Shapirovskii B.E.: On dense subspaces of topological spaces (in Russian).Doklady Akad. Nauk SSSR 214 (1974), 249-252. |
| Reference:
|
[Ar1] Arhangel'skii A.V.: Bicompact sets and the topology of spaces.Soviet Mathematics, Doklady 4 (1963), 561-564. MR 0150733 |
| Reference:
|
[Ar2] Arhangel'skii A.V.: A characterization of very $k$-spaces.Czechoslovak Math. J. 18 (1968), 392-395. MR 0229194 |
| Reference:
|
[Ar3] Arhangel'skii A.V.: Hurewicz spaces, analytic sets and fan-tightness of spaces of functions.Soviet Mathematics, Doklady 33 (1986), 396-399. |
| Reference:
|
[Ba] Balogh Z.: On compact Hausdorff spaces of countable tightness.Proc. Amer. Math. Soc. 105 (1989), 755-769. Zbl 0687.54006, MR 0930252 |
| Reference:
|
[Be] Bella A.: On spaces with the property of weak approximation by points.Comment. Math. Univ. Carolinae 35 (1994), 357-360. Zbl 0808.54007, MR 1286582 |
| Reference:
|
[BY] Bella A., Yaschenko I.V.: On AP and WAP spaces.Comment. Math. Univ. Carolinae 40 (1999), 531-536. Zbl 1010.54040, MR 1732483 |
| Reference:
|
[vD] van Douwen E.K.: Applications of maximal topologies.Topology Appl. 51 (1993), 125-140. Zbl 0845.54028, MR 1229708 |
| Reference:
|
[DTTW] Dow A., Tkachenko M.G., Tkachuk V.V., Wilson R.G.: Topologies generated by discrete subspaces.preprint. Zbl 1009.54005, MR 1918105 |
| Reference:
|
[En] Engelking R.: General Topology.PWN, Warszawa, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[Fe] Fedorchuk V.V.: Fully closed mappings and the consistency of some theorems of general topology with the axioms of set theory.Mathematics in the USSR, Sbornik, 28 (1976), 1-26. Zbl 0371.54045 |
| Reference:
|
[Gr] Gruenhage G.: Stratifiable spaces are $M_2$.Topology Proc. 1 (1976), 221-226. Zbl 0389.54019, MR 0448307 |
| Reference:
|
[Ma] Malyhin V.I.: Extremally disconnected and similar groups.Soviet Mathematics, Doklady 16 (1975), 21-25. Zbl 0322.22003 |
| Reference:
|
[MSh] Mizokami T., Shimane N.: On the $M_3$ vs $M_1$ problem.Topology Appl. 105 (2000), 1-13. MR 1761082 |
| Reference:
|
[MRS] Mrówka S., Rajagopalan M., Soundararajan T.: A characterization of compact scattered spaces through chain-limits.TOPO 72, Lecture Notes in Mathematics, 378, Springer, Berlin, 1973, pp.288-297. MR 0375234 |
| Reference:
|
[PT] Pultr A., Tozzi A.: Equationally closed subframes and representations of quotient spaces.Cahiers de Topologie et Geometrie Differentielle Categoriques 34 (1993), 167-183. MR 1239466 |
| Reference:
|
[Si] Simon P.: On accumulation points.Cahiers de Topologie et Geometrie Differentielle Categoriques 35 (1994), 321-327. Zbl 0858.54008, MR 1307264 |
| . |
