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Displaying similar documents to “Non-archimedean Eberlein-Šmulian theory.”

On sequential convergence in weakly compact subsets of Banach spaces

Witold Marciszewski (1995)

Studia Mathematica

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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.

Weak orderability of second countable spaces

Valentin Gutev (2007)

Fundamenta Mathematicae

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We demonstrate that a second countable space is weakly orderable if and only if it has a continuous weak selection. This provides a partial positive answer to a question of van Mill and Wattel.

Some results and problems about weakly pseudocompact spaces

Oleg Okunev, Angel Tamariz-Mascarúa (2000)

Commentationes Mathematicae Universitatis Carolinae

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A space X is if X is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a proto-metrizable zero-dimensional space with χ ( x , X ) > ω for every x ∈ X ; (2) every locally bounded space is truly weakly pseudocompact; (3) for ω < κ < α , the κ -Lindelöfication of a discrete space of cardinality α is weakly pseudocompact if κ = κ ω .