Continuous actions of pseudocompact groups and axioms of topological group
Korovin, Alexander V.
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 335-343 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1992-01-01
Classification:  22A05,  22B05,  54B15,  54C35,  54H11 
@article{118502,
     author = {Alexander V. Korovin},
     title = {Continuous actions of pseudocompact groups and axioms of topological group},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {335-343},
     zbl = {0786.22002},
     mrnumber = {1189665},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118502}
}

Korovin, Alexander V. Continuous actions of pseudocompact groups and axioms of topological group. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 335-343. http://gdmltest.u-ga.fr/item/118502/

Arhangel'Skiĭ A.V. Topologicheskie prostranstva funktsyĭ (in Russian), Moscow, MSU, 1989.

Arhangel'Skiĭ A.V. Functional tightness, $Q$-spaces and $\tau $-embeddings, Comment. Math. Univ. Carolinae 24 (1983), 105-120. (1983) | MR 0703930

Arhangel'Skiĭ A.V.; Tkačuk V.V. Prostranstva funktsyĭ v topologii potochechnoĭ skhodimosti (in Russian), Moscow, MSU, 1985.

Asanov M.O.; Veličko N.V. Kompaktnye množestva v $C_p$ (in Russian), Comment. Math. Univ. Carolinae 22 (1981), 255-266. (1981) | MR 0620361

Bourbaki N. Topologie générale, Chapt. III, Groupes topologiques (Théorie élémentaire), Hermann, Paris, 1942. | Zbl 1107.54001

Comfort W.W.; Ross K.A. Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (3) (1966), 483-496. (1966) | MR 0207886 | Zbl 0214.28502

Douglas L. Grant The Wallace problem and continuity of the inverse in pseudocompact groups, preprint, 1987. | MR 1142798

Ellis R. Locally compact transformation groups, Duke Math. Journ. 27 (2) (1957), 119-125. (1957) | MR 0088674 | Zbl 0079.16602

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

Ivanovskiĭ L.I. Ob odnoĭ gipoteze P.S. Aleksandrova (in Russian), Dokl. Akad. Nauk SSSR 123 (3) (1959), 786-788. (1959)

Korovin A.V. Nepreryvnye deĭstvija psevdokompaktnych grupp i aksiomy topologicheskoĭ gruppy (in Russian), VINITI, N 3734-V 90 (1990).

Korovin A.V. Nepreryvnye deĭstvija abelevyh grupp i topologicheskie svoĭstva v $C_p$-teorii gruppy (in Russian), Ph.D. Thesis (Dissertation), Moscow, MSU, 1990.

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)

Namioka I. Separate continuity and joint continuity, Pacific J. Math. 51 (2) 1974 (), 513-536. | MR 0370466 | Zbl 0294.54010

Preiss D.; Simon P. A weakly pseudocompact subspaces of a Banach space is weakly compact, Comment. Math. Univ. Carolinae 15 (1974), 603-610. (1974) | MR 0374875