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On sequential convergence in weakly compact subsets of Banach spaces

Witold Marciszewski (1995)

Studia Mathematica

We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.

On sets of small measure

Kulcsárová, Ol'ga, Riečan, Beloslav (1987)

Proceedings of the 14th Winter School on Abstract Analysis

On shape

Ralph Fox (1972)

Fundamenta Mathematicae

On similarity between topologies

Artur Bartoszewicz, Małgorzata Filipczak, Andrzej Kowalski, Małgorzata Terepeta (2014)

Open Mathematics

Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.

On simple recognizing of bounded sets

Jan Hejcman (1997)

Commentationes Mathematicae Universitatis Carolinae

We characterize those uniform spaces and commutative topological groups the bounded subsets of which can be recognized by using only one uniformly continuous pseudometric.

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