Orderability in the presence of local compactness

GUTEV, Valentin

J. Math. Soc. Japan, Tome 60 (2008) no. 1, p. 741-766 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2008-07-15
Classification:  Vietoris hyperspace,  continuous selection,  weak selection,  orderable space,  semi-orderable space,  suborderable space,  topologically well-orderable subspace,  54F05,  54B20,  54C65