Displaying similar documents to “Measures of compactness in approach spaces”

On sub-, pseudo- and quasimaximal spaces

J. Schröder (1998)

Commentationes Mathematicae Universitatis Carolinae

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The structure of sub-, pseudo- and quasimaximal spaces is investigated. A method of constructing non-trivial quasimaximal spaces is presented.

Nonreflecting stationary subsets of P κ λ

Yoshihiro Abe (2000)

Fundamenta Mathematicae

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We explore the possibility of forcing nonreflecting stationary sets of P κ λ . We also present a P κ λ generalization of Kanamori’s weakly normal filters, which induces stationary reflection.

A contribution to the topological classification of the spaces Ср(X)

Robert Cauty, Tadeusz Dobrowolski, Witold Marciszewski (1993)

Fundamenta Mathematicae

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We prove that for each countably infinite, regular space X such that C p ( X ) is a Z σ -space, the topology of C p ( X ) is determined by the class F 0 ( C p ( X ) ) of spaces embeddable onto closed subsets of C p ( X ) . We show that C p ( X ) , whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set Ω α for the multiplicative Borel class M α if F 0 ( C p ( X ) ) = M α . For each ordinal α ≥ 2, we provide an example X α such that C p ( X α ) is homeomorphic to Ω α .

On extension of the group operation over the Čech-Stone compactification

Jan Jełowicki (1993)

Colloquium Mathematicae

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The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto ( β ) 2 of the group operation. We find a subclass of ultrafilters for which this extension is well-defined and give some examples of pathologies. Next, for a given locally compact group and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to...

A note on a question of Abe

Douglas Burke (2000)

Fundamenta Mathematicae

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Assuming large cardinals, we show that every κ-complete filter can be generically extended to a V-ultrafilter with well-founded ultrapower. We then apply this to answer a question of Abe.