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Valdivia compact abelian groups.

Wieslaw Kubis (2008)

RACSAM

Valdivia compacta and equivalent norms

Ondřej Kalenda (2000)

Studia Mathematica

We prove that the dual unit ball of a Banach space X is a Corson compactum provided that the dual unit ball with respect to every equivalent norm on X is a Valdivia compactum. As a corollary we show that the dual unit ball of a Banach space X of density $ℵ_{1}$ is Corson if (and only if) X has a projectional resolution of the identity with respect to every equivalent norm. These results answer questions asked by M. Fabian, G. Godefroy and V. Zizler and yield a converse to Amir-Lindenstrauss’ theorem.

Variations of uniform completeness related to realcompactness

Miroslav Hušek (2017)

Commentationes Mathematicae Universitatis Carolinae

Various characterizations of realcompactness are transferred to uniform spaces giving non-equivalent concepts. Their properties, relations and characterizations are described in this paper. A Shirota-like characterization of certain uniform realcompactness proved by Garrido and Meroño for metrizable spaces is generalized to uniform spaces. The paper may be considered as a unifying survey of known results with some new results added.

Variations on the Banach-Stone theorem.

M. Isabel Garrido, Jesús A. Jaramillo (2002)

Extracta Mathematicae

Various kinds of local connectedness.

Charatonik, Janusz J., Illanes, Alejandro (2002)

Mathematica Pannonica

Verallgemeinerte topogene Ordnungen.

Dieter Leseberg (1985)

Monatshefte für Mathematik

Vietoris topology on spaces dominated by second countable ones

Carlos Islas, Daniel Jardon (2015)

Open Mathematics

For a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = FK : K ∈ C(M) ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂ FL for any K;L ∈ C(M). A space X is strongly dominated by a space M if there exists an M-ordered compact cover F such that for any compact K ⊂ X there is F ∈ F such that K ⊂ F . Let K(X) D C(X){Øbe the set of all nonempty compact subsets of a space...