Orderability in the presence of local compactness

概要

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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 Wattels 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.
社団法人日本数学会の論文
2008-07-01