Almost all submaximal groups are paracompact and σ-discrete

• Autorzy: O. T. Alas , I. V. Protasov , M. G. Tkačenko , V. V. Tkachuk , R. G. Wilson , I. V. Yaschenko
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

submaximality; maximality; paracompactness; topological group; separability; σ-discrete; strongly σ-discrete

Kategorie tematyczne

• 54G05: Extremally disconnected spaces, F -spaces, etc.
• 22A05: Structure of general topological groups
• 54H11: Topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 156
• Numer: 3
• Strony: 241-260

Daty

wydano

1998

otrzymano

1996-12-12

poprawiono

1997-07-10

poprawiono

1998-01-13

Twórcy

autor

O. T. Alas

• Instituto de Matemática e Estatística, Universidade de São Paulo C.P.66281, 05315-970 São Paulo, Brasil,

autor

I. V. Protasov

• Department of Cybernetics, Kiev State University, Vladimirskaya, 64, 252017 Kiev, Ukraine,

autor

M. G. Tkačenko

• Departamento de Matematicas, Universidad Autónoma Metropolitana, Av. Michoacan y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México D.F.,

autor

V. V. Tkachuk

• Departamento de Matematicas, Universidad Autónoma Metropolitana, Av. Michoacan y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México D.F.,

autor

R. G. Wilson

• Departamento de Matematicas, Universidad Autónoma Metropolitana, Av. Michoacan y La Purísima, Iztapalapa, A.P. 55-532, C.P. 09340, México D.F.,

autor

I. V. Yaschenko

• 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.