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April, 2003 Selections and sandwich-like properties via semi-continuous Banach-valued functions
Valentin GUTEV, Haruto OHTA, Kaori YAMAZAKI
J. Math. Soc. Japan 55(2): 499-521 (April, 2003). DOI: 10.2969/jmsj/1191419128


We introduce lower and upper semi-continuity of a map to the Banach space c0(λ) for an infinite cardinal λ. We prove that the following conditions (i), (ii) and (iii) on a T1-space X are equivalent: (i) For every two maps g,h : Xc0(λ) such that g is upper semi-continuous, h is lower semi-continuous and gh, there exists a continuous map f : Xc0(λ), with gfh. (ii) For every Banach space Y, with w(Y)λ, every lower semi-continuous set-valued mapping : XCc(Y) admits a continuous selection, where Cc(Y) is the set of all non-empty compact convex sets in Y. (iii)X is normal and every locally finite family F of subsets of X, with |F|λ, has a locally finite open expansion provided it has a point-finite open expansion. We also characterize several paracompact-like properties by inserting continuous maps between semi-continuous Banach-valued functions.


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Valentin GUTEV. Haruto OHTA. Kaori YAMAZAKI. "Selections and sandwich-like properties via semi-continuous Banach-valued functions." J. Math. Soc. Japan 55 (2) 499 - 521, April, 2003.


Published: April, 2003
First available in Project Euclid: 3 October 2007

zbMATH: 1039.54012
MathSciNet: MR1961298
Digital Object Identifier: 10.2969/jmsj/1191419128

Primary: ‎54C60‎
Secondary: 46B25 , 54C65 , 54D15

Keywords: Banach space , collectionwise normal , insertion , paracompact , perfectly normal countably paracompact , selection , semi-continuous

Rights: Copyright © 2003 Mathematical Society of Japan


Vol.55 • No. 2 • April, 2003
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