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July, 2008 Orderability in the presence of local compactness
Valentin GUTEV
J. Math. Soc. Japan 60(3): 741-766 (July, 2008). DOI: 10.2969/jmsj/06030741

Abstract

We prove that a locally compact paracompact space is suborderable if and only if it has a continuous weak selection. This fits naturally into the pattern of the van Mill and Wattel's characterization [15] of compact orderable spaces, and provides a further partial positive answer to a question of theirs. Several applications about the orderability and suborderablity of locally compact spaces are demonstrated. In particular, we show that a locally compact paracompact space has a continuous selection for its Vietoris hyperspace of nonempty closed subsets if and only if it is a topologically well-orderable subspace of some orderable space.

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Valentin GUTEV. "Orderability in the presence of local compactness." J. Math. Soc. Japan 60 (3) 741 - 766, July, 2008. https://doi.org/10.2969/jmsj/06030741

Information

Published: July, 2008
First available in Project Euclid: 4 August 2008

zbMATH: 1148.54014
MathSciNet: MR2440412
Digital Object Identifier: 10.2969/jmsj/06030741

Subjects:
Primary: 54F05
Secondary: 54B20 , 54C65

Keywords: continuous selection , orderable space , semi-orderable space , suborderable space , topologically well-orderable subspace , Vietoris hyperspace , weak selection

Rights: Copyright © 2008 Mathematical Society of Japan

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Vol.60 • No. 3 • July, 2008
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