Displaying similar documents to “On homological classification of pomonoids by GP-po-flatness ofS-posets”

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.

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...

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.

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.