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

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