Almost closed sets and topologies they determine
Tkachuk, Vladimir Vladimirovich ; Yashchenko, Ivan V.
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 395-405 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2001-01-01
Classification:  54A25,  54D20,  54D55,  54G12 
@article{119254,
     author = {Vladimir Vladimirovich Tkachuk and Ivan V. Yashchenko},
     title = {Almost closed sets and topologies they determine},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {395-405},
     zbl = {1053.54004},
     mrnumber = {1832158},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119254}
}

Tkachuk, Vladimir Vladimirovich; Yashchenko, Ivan V. Almost closed sets and topologies they determine. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 395-405. http://gdmltest.u-ga.fr/item/119254/

Amirdzhanov G.P.; Shapirovskii B.E. On dense subspaces of topological spaces (in Russian), Doklady Akad. Nauk SSSR 214 (1974), 249-252. (1974)

Arhangel'Skii A.V. Bicompact sets and the topology of spaces, Soviet Mathematics, Doklady 4 (1963), 561-564. (1963) | MR 0150733

Arhangel'Skii A.V. A characterization of very $k$-spaces, Czechoslovak Math. J. 18 (1968), 392-395. (1968) | MR 0229194

Arhangel'Skii A.V. Hurewicz spaces, analytic sets and fan-tightness of spaces of functions, Soviet Mathematics, Doklady 33 (1986), 396-399. (1986)

Balogh Z. On compact Hausdorff spaces of countable tightness, Proc. Amer. Math. Soc. 105 (1989), 755-769. (1989) | MR 0930252 | Zbl 0687.54006

Bella A. On spaces with the property of weak approximation by points, Comment. Math. Univ. Carolinae 35 (1994), 357-360. (1994) | MR 1286582 | Zbl 0808.54007

Bella A.; Yaschenko I.V. On AP and WAP spaces, Comment. Math. Univ. Carolinae 40 (1999), 531-536. (1999) | MR 1732483 | Zbl 1010.54040

Van Douwen E.K. Applications of maximal topologies, Topology Appl. 51 (1993), 125-140. (1993) | MR 1229708 | Zbl 0845.54028

Dow A.; Tkachenko M.G.; Tkachuk V.V.; Wilson R.G. Topologies generated by discrete subspaces, preprint. | MR 1918105 | Zbl 1009.54005

Engelking R. General Topology, PWN, Warszawa, 1977. | MR 0500780 | Zbl 0684.54001

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

Gruenhage G. Stratifiable spaces are $M_2$, Topology Proc. 1 (1976), 221-226. (1976) | MR 0448307 | Zbl 0389.54019

Malyhin V.I. Extremally disconnected and similar groups, Soviet Mathematics, Doklady 16 (1975), 21-25. (1975) | Zbl 0322.22003

Mizokami T.; Shimane N. On the $M_3$ vs $M_1$ problem, Topology Appl. 105 (2000), 1-13. (2000) | MR 1761082

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

Pultr A.; Tozzi A. Equationally closed subframes and representations of quotient spaces, Cahiers de Topologie et Geometrie Differentielle Categoriques 34 (1993), 167-183. (1993) | MR 1239466

Simon P. On accumulation points, Cahiers de Topologie et Geometrie Differentielle Categoriques 35 (1994), 321-327. (1994) | MR 1307264 | Zbl 0858.54008