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Selections and suborderability

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Artico G., Marconi U., Pelant J., Rotter L., Tkachenko M.

Fundamenta Mathematicae

2002

tom 175

nr 1

1-33

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. Extending Fujii-Nogura results, we show that an almost compact space with a continuous zero-selection is homeomorphic to some ordinal space, and a (locally compact) pseudocompact space with a continuous zero-selection is an (open) subspace of some space of ordinals. Under the Diamond Principle, we construct several counterexamples, e.g. a locally compact locally countable monotonically normal space with a continuous zero-selection which is not suborderable.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Artico G.

1 Marconi U.

1 Pelant J.

1 Rotter L.

1 Tkachenko M.

1 2002

Wyniki wyszukiwania

Selections and suborderability