Non-archimedean Eberlein-Šmulian theory.

Kiyosawa, T.; Schikhof, W.H.

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About an example of a Banach space not weaky K-analytic.

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Witold Marciszewski (1995)

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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)

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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.

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Leonidas Tsitsas (1977)

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Some results and problems about weakly pseudocompact spaces

Oleg Okunev, Angel Tamariz-Mascarúa (2000)

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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 $x \in X$ ; (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 $κ = κ^{ω}$ .