On resolvable spaces and groups

Luis Miguel Villegas-Silva

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 3, page 579-584
  • ISSN: 0010-2628

Abstract

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It is proved that every uncountable ω -bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.

How to cite

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Villegas-Silva, Luis Miguel. "On resolvable spaces and groups." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 579-584. <http://eudml.org/doc/247763>.

@article{Villegas1995,
abstract = {It is proved that every uncountable $\omega $-bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.},
author = {Villegas-Silva, Luis Miguel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {resolvable; maximal; $\alpha $-bounded; resolvable space; maximal space; topological space; -bounded topological group; homogeneous space; Booth's lemma; non-discrete irresolvable topological group; extremally disconnected},
language = {eng},
number = {3},
pages = {579-584},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On resolvable spaces and groups},
url = {http://eudml.org/doc/247763},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Villegas-Silva, Luis Miguel
TI - On resolvable spaces and groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 579
EP - 584
AB - It is proved that every uncountable $\omega $-bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.
LA - eng
KW - resolvable; maximal; $\alpha $-bounded; resolvable space; maximal space; topological space; -bounded topological group; homogeneous space; Booth's lemma; non-discrete irresolvable topological group; extremally disconnected
UR - http://eudml.org/doc/247763
ER -

References

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  10. Guran I.I., On topological groups close to being Lindelöf, Soviet Math. Dokl. 23 (1981), 173-175. (1981) Zbl0478.22002
  11. Hewitt E., A problem of set-theoretic topology, Duke Math. J. 10 (1943), 309-333. (1943) Zbl0060.39407MR0008692
  12. Louveau A., Sur un article de S. Sirota, Bull. Sci. Math. (2) 96 (1972), 3-7. (1972) Zbl0228.54032MR0308326
  13. Malykhin V.I., Extremally disconnected and similar groups, Soviet Math. Dokl. 16 (1975), 21-25. (1975) Zbl0322.22003
  14. Padmavally K., An example of a connected irresolvable Hausdorff spaces, Duke Math. J. 20 (1953), 513-520. (1953) MR0059539

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