Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
241-260
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-12-12
poprawiono
1997-07-10
poprawiono
1998-01-13
Twórcy
autor
- Instituto de Matemática e Estatística, Universidade de São Paulo C.P.66281, 05315-970 São Paulo, Brasil
autor
- Department of Cybernetics, Kiev State University, Vladimirskaya, 64, 252017 Kiev, Ukraine
autor
- Departamento de Matematicas, Universidad Autónoma Metropolitana, Av. Michoacan y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México D.F.
autor
- Departamento de Matematicas, Universidad Autónoma Metropolitana, Av. Michoacan y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México D.F.
autor
- Departamento de Matematicas, Universidad Autónoma Metropolitana, Av. Michoacan y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México D.F.
autor
- Moscow Center for Continuous, Mathematical Education, B. Vlas’evskiĭ, 11, 121002 Moscow, Russia
Bibliografia
- [ArCo] A. V. Arhangel'skiĭ [A. V. Arkhangel'skiĭ] and P. J. Collins, z On submaximal spaces, Topology Appl. 64 (1995), 219-241.
- [CoLF] W. W. Comfort and L. Feng, z The union of resolvable spaces is resolvable, Math. Japon. 38 (1993), 413-414.
- [CoRo] W. W. Comfort and K. A. Ross, z Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (1966), 483-496.
- [vD] E. K. van Douwen, z Applications of minimal topologies, Topology Appl. 51 (1993), 125-139.
- [En] R. Engelking, z General Topology, PWN, Warszawa, 1977.
- [GRS] J. A. Guthrie, D. F. Reynolds and H. E. Stone, z Connected expansions of topologies, Bull. Austral. Math. Soc. 9 (1973), 259-265.
- [Gu] I. Guran, z On topological groups close to being Lindelöf, Soviet Math. Dokl. 23 (1981), 173-175.
- [He] E. Hewitt, z A problem of set-theoretic topology, Duke Math. J. 10 (1943), 309-333.
- [HeRo] E. Hewitt and K. Ross, z Abstract Harmonic Analysis, Vol. 1, Springer, Berlin, 1963.
- [Ma] V. I. Malykhin, z Extremally disconnected and similar groups, Soviet Math. Dokl. 16 (1975), 21-25.
- [Pr] I. V. Protasov, z Absolutely resolvable groups, Ukrain. Math. Zh. 48 (1996), 383-392 (in Russian).
- [Sch] J. Schröder, z On sub-, pseudo-, and quasimaximal spaces, in: Eighth Prague Topological Sympos., 1996, Abstracts, p. 22.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv156i3p241bwm