Selections that characterize topological completeness

• Autorzy: Jan van Mill , Jan Pelant , Roman Pol
• Języki publikacji: EN

Abstrakty

EN

We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].

Słowa kluczowe

EN

selection; Vietoris topology; completely metrizable

Kategorie tematyczne

• 54E50: Complete metric spaces
• 54C65: Selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1996
• Tom: 149
• Numer: 2
• Strony: 127-141

Daty

wydano

1996

otrzymano

1995-01-23

poprawiono

1995-11-17

Twórcy

autor

Jan van Mill

• Faculteit Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081 A, 1081 HV Amsterdam, The Netherlands

autor

Jan Pelant

• epartment of Mathematics, Warsaw University, Banacha 2, 00-913 Warszawa 59, Poland

autor

Roman Pol

• Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 11567 Praha 1, Czech Republic

Bibliografia

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• [5] V. Gutev, S. Nedev, J. Pelant, and V. Valov, Cantor set selectors, Topology Appl. 44 (1992), 163-168.
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