Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
$m$-topological group; semitopological group; paratopological group; topological group; topology of pointwise convergence; Eberlein compact; weak functional tightness
$m$-topological group; semitopological group; paratopological group; topological group; topology of pointwise convergence; Eberlein compact; weak functional tightness
Summary:
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.
References:
[1] Arhangel'skiĭ A.V.: Topologicheskie prostranstva funktsyĭ (in Russian). Moscow, MSU, 1989.
[2] Arhangel'skiĭ A.V.: Functional tightness, $Q$-spaces and $\tau $-embeddings. Comment. Math. Univ. Carolinae 24 (1983), 105-120. MR 0703930
[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. MR 0620361
[5] Bourbaki N.: Topologie générale. Chapt. III, Groupes topologiques (Théorie élémentaire), Hermann, Paris, 1942. Zbl 1107.54001
[6] Comfort W.W., Ross K.A.: Pseudocompactness and uniform continuity in topological groups. Pacific J. Math. 16 (3) (1966), 483-496. MR 0207886 | Zbl 0214.28502
[7] Douglas L. Grant: The Wallace problem and continuity of the inverse in pseudocompact groups. preprint, 1987. MR 1142798
[8] Ellis R.: Locally compact transformation groups. Duke Math. Journ. 27 (2) (1957), 119-125. MR 0088674 | Zbl 0079.16602
[9] Engelking R.: General Topology. Warszawa, PWN, 1977. MR 0500780 | Zbl 0684.54001
[10] Ivanovskiĭ L.I.: Ob odnoĭ gipoteze P.S. Aleksandrova (in Russian). Dokl. Akad. Nauk SSSR 123 (3) (1959), 786-788.
[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.
[14] Namioka I.: Separate continuity and joint continuity. Pacific J. Math. 51 (2) 1974 (), 513-536. MR 0370466 | Zbl 0294.54010
[15] Preiss D., Simon P.: A weakly pseudocompact subspaces of a Banach space is weakly compact. Comment. Math. Univ. Carolinae 15 (1974), 603-610. MR 0374875
Search
Partner of
