King spaces and compactness
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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 phrasesVietoris topology continuous weak selection king space pseudocompact locally compact
Mathematics Subject Classification54B20 54C65 54D30 54F05
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- 7.V. Gutev, Selections and hyperspaces, in: Recent Progress in General Topology, III (K. P. Hart, J. van Mill and P. Simon, eds.), Atlantis Press, Springer (2014), pp. 535–579.Google Scholar
- 12.H. Kok, Connected Orderable Spaces, Mathematical Centre Tracts, No. 49, Mathematisch Centrum (Amsterdam, 1973).Google Scholar