Almost closed sets and topologies they determine

Vladimir Vladimirovich Tkachuk; Ivan V. Yashchenko

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 2, page 395-405
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Tkachuk, Vladimir Vladimirovich, and Yashchenko, Ivan V.. "Almost closed sets and topologies they determine." Commentationes Mathematicae Universitatis Carolinae 42.2 (2001): 395-405. <http://eudml.org/doc/248804>.

@article{Tkachuk2001,
abstract = {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.},
author = {Tkachuk, Vladimir Vladimirovich, Yashchenko, Ivan V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {AP-space; WAP-space; scattered space; countably compact space; function space; discretely generated space; AP-space; WAP-space; scattered space; countably compact space; function space; discretely generated space},
language = {eng},
number = {2},
pages = {395-405},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Almost closed sets and topologies they determine},
url = {http://eudml.org/doc/248804},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Tkachuk, Vladimir Vladimirovich
AU - Yashchenko, Ivan V.
TI - Almost closed sets and topologies they determine
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 2
SP - 395
EP - 405
AB - 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.
LA - eng
KW - AP-space; WAP-space; scattered space; countably compact space; function space; discretely generated space; AP-space; WAP-space; scattered space; countably compact space; function space; discretely generated space
UR - http://eudml.org/doc/248804
ER -

References

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  1. Amirdzhanov G.P., Shapirovskii B.E., On dense subspaces of topological spaces (in Russian), Doklady Akad. Nauk SSSR 214 (1974), 249-252. (1974) 
  2. Arhangel'skii A.V., Bicompact sets and the topology of spaces, Soviet Mathematics, Doklady 4 (1963), 561-564. (1963) MR0150733
  3. Arhangel'skii A.V., A characterization of very k -spaces, Czechoslovak Math. J. 18 (1968), 392-395. (1968) MR0229194
  4. Arhangel'skii A.V., Hurewicz spaces, analytic sets and fan-tightness of spaces of functions, Soviet Mathematics, Doklady 33 (1986), 396-399. (1986) 
  5. Balogh Z., On compact Hausdorff spaces of countable tightness, Proc. Amer. Math. Soc. 105 (1989), 755-769. (1989) Zbl0687.54006MR0930252
  6. Bella A., On spaces with the property of weak approximation by points, Comment. Math. Univ. Carolinae 35 (1994), 357-360. (1994) Zbl0808.54007MR1286582
  7. Bella A., Yaschenko I.V., On AP and WAP spaces, Comment. Math. Univ. Carolinae 40 (1999), 531-536. (1999) Zbl1010.54040MR1732483
  8. van Douwen E.K., Applications of maximal topologies, Topology Appl. 51 (1993), 125-140. (1993) Zbl0845.54028MR1229708
  9. Dow A., Tkachenko M.G., Tkachuk V.V., Wilson R.G., Topologies generated by discrete subspaces, preprint. Zbl1009.54005MR1918105
  10. Engelking R., General Topology, PWN, Warszawa, 1977. Zbl0684.54001MR0500780
  11. 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. Zbl0371.54045
  12. Gruenhage G., Stratifiable spaces are M 2 , Topology Proc. 1 (1976), 221-226. (1976) Zbl0389.54019MR0448307
  13. Malyhin V.I., Extremally disconnected and similar groups, Soviet Mathematics, Doklady 16 (1975), 21-25. (1975) Zbl0322.22003
  14. Mizokami T., Shimane N., On the M 3 vs M 1 problem, Topology Appl. 105 (2000), 1-13. (2000) MR1761082
  15. 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. MR0375234
  16. Pultr A., Tozzi A., Equationally closed subframes and representations of quotient spaces, Cahiers de Topologie et Geometrie Differentielle Categoriques 34 (1993), 167-183. (1993) MR1239466
  17. Simon P., On accumulation points, Cahiers de Topologie et Geometrie Differentielle Categoriques 35 (1994), 321-327. (1994) Zbl0858.54008MR1307264

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