Continuous actions of pseudocompact groups and axioms of topological group

Alexander V. Korovin

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 2, page 335-343
  • ISSN: 0010-2628

Abstract

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In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class 𝒩 of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces 𝒩 that gives some new examples and statements for the C p -theory and theory of topologically homogeneous spaces.

How to cite

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Korovin, Alexander V.. "Continuous actions of pseudocompact groups and axioms of topological group." Commentationes Mathematicae Universitatis Carolinae 33.2 (1992): 335-343. <http://eudml.org/doc/247414>.

@article{Korovin1992,
abstract = {In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class $\mathcal \{N\}$ of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces $\mathcal \{N\}$ that gives some new examples and statements for the $C_p$-theory and theory of topologically homogeneous spaces.},
author = {Korovin, Alexander V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$m$-topological group; semitopological group; paratopological group; topological group; topology of pointwise convergence; Eberlein compact; weak functional tightness; topological group; paratopological group; Eberlein compact; continuous multiplication},
language = {eng},
number = {2},
pages = {335-343},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Continuous actions of pseudocompact groups and axioms of topological group},
url = {http://eudml.org/doc/247414},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Korovin, Alexander V.
TI - Continuous actions of pseudocompact groups and axioms of topological group
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 2
SP - 335
EP - 343
AB - In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class $\mathcal {N}$ of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces $\mathcal {N}$ that gives some new examples and statements for the $C_p$-theory and theory of topologically homogeneous spaces.
LA - eng
KW - $m$-topological group; semitopological group; paratopological group; topological group; topology of pointwise convergence; Eberlein compact; weak functional tightness; topological group; paratopological group; Eberlein compact; continuous multiplication
UR - http://eudml.org/doc/247414
ER -

References

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  1. Arhangel'skiĭ A.V., Topologicheskie prostranstva funktsyĭ (in Russian), Moscow, MSU, 1989. 
  2. Arhangel'skiĭ A.V., Functional tightness, Q -spaces and τ -embeddings, Comment. Math. Univ. Carolinae 24 (1983), 105-120. (1983) MR0703930
  3. Arhangel'skiĭ A.V., Tkačuk V.V., Prostranstva funktsyĭ v topologii potochechnoĭ skhodimosti (in Russian), Moscow, MSU, 1985. 
  4. Asanov M.O., Veličko N.V., Kompaktnye množestva v C p (in Russian), Comment. Math. Univ. Carolinae 22 (1981), 255-266. (1981) MR0620361
  5. Bourbaki N., Topologie générale, Chapt. III, Groupes topologiques (Théorie élémentaire), Hermann, Paris, 1942. Zbl1107.54001
  6. Comfort W.W., Ross K.A., Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (3) (1966), 483-496. (1966) Zbl0214.28502MR0207886
  7. Douglas L. Grant, The Wallace problem and continuity of the inverse in pseudocompact groups, preprint, 1987. MR1142798
  8. Ellis R., Locally compact transformation groups, Duke Math. Journ. 27 (2) (1957), 119-125. (1957) Zbl0079.16602MR0088674
  9. Engelking R., General Topology, Warszawa, PWN, 1977. Zbl0684.54001MR0500780
  10. Ivanovskiĭ L.I., Ob odnoĭ gipoteze P.S. Aleksandrova (in Russian), Dokl. Akad. Nauk SSSR 123 (3) (1959), 786-788. (1959) 
  11. Korovin A.V., Nepreryvnye deĭstvija psevdokompaktnych grupp i aksiomy topologicheskoĭ gruppy (in Russian), VINITI, N 3734-V 90 (1990). 
  12. Korovin A.V., Nepreryvnye deĭstvija abelevyh grupp i topologicheskie svoĭstva v C p -teorii gruppy (in Russian), Ph.D. Thesis (Dissertation), Moscow, MSU, 1990. 
  13. Kuz'minov V.I., O gipoteze P.S. Aleksandrova v teorii topologicheskich grupp (in Russian), Dokl. Akad. Nauk SSSR 125 (3) (1959), 727-729. (1959) 
  14. Namioka I., Separate continuity and joint continuity, Pacific J. Math. 51 (2) 1974 (), 513-536. Zbl0294.54010MR0370466
  15. Preiss D., Simon P., A weakly pseudocompact subspaces of a Banach space is weakly compact, Comment. Math. Univ. Carolinae 15 (1974), 603-610. (1974) MR0374875

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