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Tytuł artykułu

Selections and suborderability

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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. 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.
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Twórcy
  • Dipartimento di Matematica Pura e Applicata, via Belzoni 7, I-35131 Padova, Italy
  • Dipartimento di Matematica Pura e Applicata, via Belzoni 7, I-35131 Padova, Italy
autor
  • Mathematical Institute, Academy of Sciences of Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic
autor
  • Dipartimento di Matematica Pura e Applicata, via Belzoni 7, I-35131 Padova, Italy
  • Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco #186, Col. Vicentina, C.P. 09340 Iztapalapa, México, D.F., México
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-1-1
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