An Example Concerning Valdivia Compact Spaces

Kalenda, Ondrej. "An Example Concerning Valdivia Compact Spaces." Serdica Mathematical Journal 25.2 (1999): 131-140. <http://eudml.org/doc/11510>.

@article{Kalenda1999,
abstract = {∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998We 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.},
author = {Kalenda, Ondrej},
journal = {Serdica Mathematical Journal},
keywords = {Valdivia Compact Space; Fréchet-Urysohn Space; Countably Compact Space; Countably 1-Norming Markusevic Basis; Valdivia compact spaces; Fréchet-Urysohn spaces; countably compact spaces; Markuševič basis},
language = {eng},
number = {2},
pages = {131-140},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {An Example Concerning Valdivia Compact Spaces},
url = {http://eudml.org/doc/11510},
volume = {25},
year = {1999},
}

TY - JOUR
AU - Kalenda, Ondrej
TI - An Example Concerning Valdivia Compact Spaces
JO - Serdica Mathematical Journal
PY - 1999
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 25
IS - 2
SP - 131
EP - 140
AB - ∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998We 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.
LA - eng
KW - Valdivia Compact Space; Fréchet-Urysohn Space; Countably Compact Space; Countably 1-Norming Markusevic Basis; Valdivia compact spaces; Fréchet-Urysohn spaces; countably compact spaces; Markuševič basis
UR - http://eudml.org/doc/11510
ER -