Topological Games and Hyperspace Topologies
Copyright policy )Topological Games and Hyperspace Topologies
The author uses the ``approach spaces'' of \textit{R. Lowen} [Approach spaces: the missing link in the topology-uniformity-metric triad (1997; Zbl 0891.54001)] to give a unified treatment of various hypertopologies and their properties such as separation axioms, metrizability etc. He then studies the links between topological games and the properties of hypertopologies with particular reference to Polishness. The paper is a valuable addition to the ever growing literature on the subject. Reviewer's remark: The proximal ball topology was discovered by \textit{G. Di Maio} and the reviewer [Rend. Ist. Mat. Univ. Trieste 22, No. 1-2, 140-161 (1990; Zbl 0793.54009)]. The news of its discovery was conveyed to colleages whose papers appeared earlier or contemporaneously with the above paper.
- University of North Carolina System United States
- University of North Carolina at Pembroke United States
Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.), approach spaces, Baire category, Baire spaces, Lower separation axioms (\(T_0\)--\(T_3\), etc.), Games involving topology, set theory, or logic, Metric spaces, metrizability, separation axioms, Topological spaces and generalizations (closure spaces, etc.), hyperspace, Hyperspaces in general topology, topological games, metrizability
Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.), approach spaces, Baire category, Baire spaces, Lower separation axioms (\(T_0\)--\(T_3\), etc.), Games involving topology, set theory, or logic, Metric spaces, metrizability, separation axioms, Topological spaces and generalizations (closure spaces, etc.), hyperspace, Hyperspaces in general topology, topological games, metrizability
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