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 ${m_f}(A) = \inf \{ f(x):x \in A\}$.References
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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