Journal of the Mathematical Society of Japan

Orderability in the presence of local compactness

Valentin GUTEV

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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.

Article information

J. Math. Soc. Japan, Volume 60, Number 3 (2008), 741-766.

First available in Project Euclid: 4 August 2008

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Zentralblatt MATH identifier

Primary: 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]
Secondary: 54B20: Hyperspaces 54C65: Selections [See also 28B20]

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


GUTEV, Valentin. Orderability in the presence of local compactness. J. Math. Soc. Japan 60 (2008), no. 3, 741--766. doi:10.2969/jmsj/06030741.

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