Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 60, Number 3 (2008), 741-766.
Orderability in the presence of local compactness
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  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.
J. Math. Soc. Japan, Volume 60, Number 3 (2008), 741-766.
First available in Project Euclid: 4 August 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
GUTEV, Valentin. Orderability in the presence of local compactness. J. Math. Soc. Japan 60 (2008), no. 3, 741--766. doi:10.2969/jmsj/06030741. https://projecteuclid.org/euclid.jmsj/1217884491