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Total paracompactness and Banach spaces.

Lupianez, Francisco Gallego (1988) Total paracompactness and Banach spaces. Proceedings of the American Mathematical Society, 103 (1). pp. 210-214. ISSN 0002-9939

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Abstract

In this paper, we study some problems related to the Corson
theorem. In particular we prove that co does not fulfil such a theorem; hence this theorem is not valid for all infinite-dimensional Banach spaces. We give also generalizations of Corson's theorem for some infinite-dimensional normed spaces.

Item Type:Article
Additional Information:The results of this paper are contained in the author's Doctoral Thesis, directed by Professor E. Outerelo, to whom the author expresses his hearty thanks for his help in the preparation of this paper.
Uncontrolled Keywords:Open basis; Locally finite covering; Banach spaces; Bounded convex sets; Normed spaces, Total paracompactness.
Subjects:Sciences > Mathematics > Topology
ID Code:15334
References:

S. Banach, Th6orie des operations lin6aires, 2nd ed., Chelsea, New York, 1978.

H. H. Corson, Collections of convex sets which cover a Banach space, Fund. Math. 49 (1961), 143-145.

H. H. Corson, T. J. McMinn, E. A. Michael, and J. I.Nagata, Bases and local finiteness, Notices Amer. Math. Soc. 6(1959), 814.

D. W. Curtis, Total and absolute paracompactness, Fund. Math. 77 (1973), 277-293.

R. M. Ford, Basis properties in dimension theory, Doctoral Dissertation, Auburn Univ., 1963.

R. B. Holmes, Geometrical functional analysis and its applications, Springer-Verlag, New York, 1975.

J. Horwath, Topological vector spaces and distributions. I, Addison-Wesley, Reading, Mass., 1966.

W. Hurewicz and H. Wallrnan, Dimension theory, 5th ed., Princeton Univ. Press, Princeton, N.J., 1941.

A. Pelczyn'ski, MR 23 # A2732.

H. Toruiiczyk, Smooth partitions of unity on some nonseparable Banach spaces, Studia Math.46 (1973), 43-51.

Deposited On:24 May 2012 09:52
Last Modified:30 Oct 2013 19:07

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