Displaying similar documents to “Locally compact realcompactifications”

Selections and suborderability

Giuliano Artico, Umberto Marconi, Jan Pelant, Luca Rotter, Mikhail Tkachenko (2002)

Fundamenta Mathematicae

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We extend van Mill-Wattel's results and show that each countably compact completely regular space with a continuous selection on couples is suborderable. The result extends also to pseudocompact spaces if they are either scattered, first countable, or connected. An infinite pseudocompact topological group with such a continuous selection is homeomorphic to the Cantor set. A zero-selection is a selection on the hyperspace of closed sets which chooses always an isolated point of a set....