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Uniform Properties and Hyperspaces of Metrizable Spaces
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C. Costantini
Published/Copyright:
June 4, 2010
Abstract
Two equivalent metrics can be compared, with respect to their uniform properties, in several different ways. We present some of them, and then use one of these conditions to characterize which metrics on a space induce the same lower Hausdorff topology on the hyperspace. Finally, we focus our attention to complete metrics.
Key words and phrases.: Metrizable space; hyperspace; lower Hausdorff topology; Hausdorff metric topology; equivalent metrics; uniformly equivalent metrics; gap; totally bounded set; complete subspace; uniformly discrete set; wide family of sets
Received: 1998-05-18
Revised: 1998-10-09
Published Online: 2010-06-04
Published in Print: 1999-December
© Heldermann Verlag
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Articles in the same Issue
- Domains of Attraction on Sturm–Liouville Hypergroups of Polynomial Growth
- On the Products of Bounded Darboux Baire One Functions
- Uniform Properties and Hyperspaces of Metrizable Spaces
- Existence of Solutions and L∞–Bounds for Quasilinear Degenerate Parabolic Systems
- Killing Residual Measures
- An Intersection Formula for the Normal Cone Associated with the Hypertangent Cone
- Multiplication of Schwartz Distributions and Colombeau Generalized Functions
- Oscillation of the Solutions of Nonlinear Impulsive Differential Equations of the First Order with Advanced Argument
- An Upper Bound of the Mean Growth in the Williams–Bjerknes Tumour Model
- Fixed Point Theorems for Metrically Weakly Inward Set–Valued Mappings
