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Covering a Banach space
Author(s):
Vladimir
P.
Fonf;
Clemente
Zanco
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2607-2611.
MSC (2000):
Primary 46B20;
Secondary 54E52
Posted:
February 17, 2006
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Abstract:
A well-known theorem by H. Corson states that if a Banach space admits a locally finite covering by bounded closed convex subsets, then it contains no infinite-dimensional reflexive subspace. We strengthen this result proving that if an infinite-dimensional Banach space admits a locally finite covering by bounded  -closed subsets, then it is  -saturated, thus answering a question posed by V. Klee concerning locally finite coverings of  spaces. Moreover, we provide information about massiveness of the set of singular points in (PC) spaces.
References:
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Additional Information:
Vladimir
P.
Fonf
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel
Email:
fonf@math.bgu.ac.il
Clemente
Zanco
Affiliation:
Dipartimento di Matematica, Università degli Studi, via C. Saldini 50, 20133 Milano MI, Italy
Email:
zanco@mat.unimi.it
DOI:
10.1090/S0002-9939-06-08254-2
PII:
S 0002-9939(06)08254-2
Keywords:
Covering,
locally finite covering,
space $c_0$,
(PC) property
Received by editor(s):
October 20, 2004
Received by editor(s) in revised form:
March 22, 2005
Posted:
February 17, 2006
Additional Notes:
The first author was supported in part by Israel Science Foundation, Grant \#139/03.
The second author was supported in part by the Ministero dell'Università e della Ricerca Scientifica e Tecnologica of Italy
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2006,
American Mathematical Society
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