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Displaying similar documents to “Weak countable compactness implies quasi-weak drop property”

On weak drop property and quasi-weak drop property

J. H. Qiu (2003)

Studia Mathematica

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Every weakly sequentially compact convex set in a locally convex space has the weak drop property and every weakly compact convex set has the quasi-weak drop property. An example shows that the quasi-weak drop property is strictly weaker than the weak drop property for closed bounded convex sets in locally convex spaces (even when the spaces are quasi-complete). For closed bounded convex subsets of quasi-complete locally convex spaces, the quasi-weak drop property is equivalent to weak...

On the quasi-weak drop property

J. H. Qiu (2002)

Studia Mathematica

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A new drop property, the quasi-weak drop property, is introduced. Using streaming sequences introduced by Rolewicz, a characterisation of the quasi-weak drop property is given for closed bounded convex sets in a Fréchet space. From this, it is shown that the quasi-weak drop property is equivalent to weak compactness. Thus a Fréchet space is reflexive if and only if every closed bounded convex set in the space has the quasi-weak drop property.

Drop property on locally convex spaces

Ignacio Monterde, Vicente Montesinos (2008)

Studia Mathematica

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A single technique provides short proofs of some results about drop properties on locally convex spaces. It is shown that the quasi drop property is equivalent to a drop property for countably closed sets. As a byproduct, we prove that the drop and quasi drop properties are separably determined.

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.

Selections and weak orderability

Michael Hrušák, Iván Martínez-Ruiz (2009)

Fundamenta Mathematicae

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We answer a question of van Mill and Wattel by showing that there is a separable locally compact space which admits a continuous weak selection but is not weakly orderable. Furthermore, we show that a separable space which admits a continuous weak selection can be covered by two weakly orderable spaces. Finally, we give a partial answer to a question of Gutev and Nogura by showing that a separable space which admits a continuous weak selection admits a continuous selection for all finite...