Displaying similar documents to “A comparison of weak and strong continuity”

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.

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...