Acta Mathematica Hungarica

, Volume 152, Issue 1, pp 1–10 | Cite as

King spaces and compactness

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Abstract

Using the framework of weak selections, Nagao and Shakhmatov introduced topological king spaces, and extended the classical “King Chicken Theorem” by showing that each compact space with a continuous weak selection is a king space. They also obtained that several king spaces are compact, and raised the question whether every locally compact (or locally pseudocompact) king space must be compact. In the present paper, we settle this question in the affirmative.

Key words and phrases

Vietoris topology continuous weak selection king space pseudocompact locally compact 

Mathematics Subject Classification

54B20 54C65 54D30 54F05 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of MaltaMsidaMalta

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