Topological Games and Hyperspace Topologies

UNCP Author/Contributor (non-UNCP co-authors, if there are any, appear on document)
Dr. Laszlo Zsilinszky, Professor (Creator)
The University of North Carolina at Pembroke (UNCP )
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Abstract: The paper proposes a uni?ed description of hypertopologies, i.e. topologies on the nonempty closed subsets of a topological space, based on the notion of approach spaces introduced by R. Lowen. As a special case of this description we obtain the abstract hit-and-miss, proximal hit-and-miss and a big portion of weak hypertopologies generated by gap and excess functionals (including the Wijsman topology and the ?nite Hausdorff topology), respectively. We also give characterizations of separation axioms T0,T1,T2,T3 and complete regularity as well as of metrizability of hypertopologies in this general setting requiring no additional conditions. All this is done to provide a background for proving the main results in Section 4, where we apply topological games (the Banach–Mazur and the strong Choquet game, respectively) to establish various properties of hypertopologies; in particular we characterize Polishness of hypertopologies in this general setting

Additional Information

Kluwer Academic Publishers Set-Valued Analysis Vol 6: 187–207
Language: English
Date: 1998
approach spaces, (proximal) hit-and-miss topologies, weak hypertopologies, separation axioms, metrizability, Banach–Mazur game, strong Choquet game, (strongly) a-favorable spaces, Polish spaces.

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