Displaying similar documents to “Selections and weak orderability”

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.

Weak Cauchy sequences in L ∞ ( μ , X )

Georg Schlüchtermann (1995)

Studia Mathematica

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For a finite and positive measure space Ω,∑,μ characterizations of weak Cauchy sequences in L ∞ ( μ , X ) , the space of μ-essentially bounded vector-valued functions f:Ω → X, are presented. The fine distinction between Asplund and conditionally weakly compact subsets of L ∞ ( μ , X ) is discussed.

The weak Phillips property

Ali Ülger (2001)

Colloquium Mathematicae

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Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.

Weak selections and weak orderability of function spaces

Valentin Gutev (2010)

Czechoslovak Mathematical Journal

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It is proved that for a zero-dimensional space X , the function space C p ( X , 2 ) has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if X is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space E , the function space C p ( X , E ) is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides...

On a dual locally uniformly rotund norm on a dual Vašák space

Marián Fabian (1991)

Studia Mathematica

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We transfer a renorming method of transfer, due to G. Godefroy, from weakly compactly generated Banach spaces to Vašák, i.e., weakly K-countably determined Banach spaces. Thus we obtain a new construction of a locally uniformly rotund norm on a Vašák space. A further cultivation of this method yields the new result that every dual Vašák space admits a dual locally uniformly rotund norm.