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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The infimal value functional and the uniformization of hit-and-miss hyperspace topologies
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by Gerald Beer and Robert Tamaki PDF
Proc. Amer. Math. Soc. 122 (1994), 601-612 Request permission

Abstract:

We give necessary and sufficient conditions for the uniformizability of hit-and-miss and proximal hit-and-miss hyperspace topologies defined on the nonempty closed subsets ${\text {CL}}(X)$ of a Hausdorff uniform space $\langle X,\mathcal {U}\rangle$. In the case of uniformizability, one can always find a family $\mathcal {F}$ of continuous functions on X into [0, 1] so that the hyperspace topology is the weak topology induced by $\{ {m_f}:f \in \mathcal {F}\}$, where for each f, ${m_f}:{\text {CL}}(X) \to [0,1]$ is the infimal value functional defined by ${m_f}(A) = \inf \{ f(x):x \in A\}$.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 122 (1994), 601-612
  • MSC: Primary 54B20
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1264804-5
  • MathSciNet review: 1264804