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Title: An Example Concerning Valdivia Compact Spaces
Authors: Kalenda, Ondrej
Keywords: Valdivia Compact Space
Fréchet-Urysohn Space
Countably Compact Space
Countably 1-Norming Markusevic Basis
Issue Date: 1999
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 25, No 2, (1999), 131p-140p
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.
Description: ∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998
ISSN: 1310-6600
Appears in Collections:Volume 25 Number 2

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