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