# An Example Concerning Valdivia Compact Spaces

Serdica Mathematical Journal (1999)

- Volume: 25, Issue: 2, page 131-140
- ISSN: 1310-6600

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topKalenda, 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 -

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