Orderability in the presence of local compactness. (English) Zbl 1148.54014

All spaces considered are at least Hausdorff. The article is motivated by results discussed in [J. van Mill and E. Wattel, Proc. Am. Math. Soc. 83, 601-605 (1981; Zbl 0473.54010)].
It is shown 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.
The author also proves that a locally compact paracompact space is suborderable if and only if it has a continuous weak selection. His investigations show that every locally compact paracompact space which has a continuous weak selection is semi-orderable, that is, is the topological sum of two orderable spaces.


54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54B20 Hyperspaces in general topology
54C65 Selections in general topology


Zbl 0473.54010
Full Text: DOI


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