Selections and suborderability

• Autorzy: Giuliano Artico , Umberto Marconi , Jan Pelant , Luca Rotter , Mikhail Tkachenko
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
• 54B20: Hyperspaces
• 54G12: Scattered spaces
• 54H11: Topological groups
• 54C65: Selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 175
• Numer: 1
• Strony: 1-33

Daty

wydano

2002

Twórcy

autor

Giuliano Artico

• Dipartimento di Matematica Pura e Applicata, via Belzoni 7, I-35131 Padova, Italy

autor

Umberto Marconi

• Dipartimento di Matematica Pura e Applicata, via Belzoni 7, I-35131 Padova, Italy

autor

Jan Pelant

• Mathematical Institute, Academy of Sciences of Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

autor

Luca Rotter

• Dipartimento di Matematica Pura e Applicata, via Belzoni 7, I-35131 Padova, Italy

autor

Mikhail Tkachenko

• Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco #186, Col. Vicentina, C.P. 09340 Iztapalapa, México, D.F., México

Identyfikatory

DOI

10.4064/fm175-1-1