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  7. An Example Concerning Valdivia Compact Spaces

An Example Concerning Valdivia Compact Spaces

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Authors: Kalenda, Ondrej
Issue Date: 1999
Citation: Serdica Mathematical Journal, Vol. 25, No 2, (1999), 131p-140p Copy to clipboard
ISSN: 1310-6600
URI: http://hdl.handle.net/10525/442 Copy to clipboard
Note:

∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998

Abstract: We prove that the dual unit ball of the space C0 [0, ω1 ) endowed with the weak* topology is not a Valdivia compact. This answers a question posed to the author by V. Zizler and has several consequences. Namely, it yields an example of an affine continuous image of a convex Valdivia compact (in the weak* topology of a dual Banach space) which is not Valdivia, and shows that the property of the dual unit ball being Valdivia is not an isomorphic property. Another consequence is that the space C0 [0, ω1 ) has no countably 1-norming Markusevic basis.
Language: en
Publisher: Institute of Mathematics and Informatics, Bulgarian Academy of SciencesSubject: Valdivia Compact SpaceFréchet-Urysohn SpaceCountably Compact SpaceCountably 1-Norming Markusevic Basis
Type: Article