King spaces and compactness
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- Gutev, V. Acta Math. Hungar. (2017) 152: 1. doi:10.1007/s10474-017-0713-7
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.