The topological type of spaces consisting of certain metrics on locally compact metrizable spaces with the compact-open topology
Katsuhisa Koshino

TL;DR
This paper characterizes the topological structure of the space of admissible metrics on certain non-compact, locally connected, separable metrizable spaces, showing it is homeomorphic to the space of sequences converging to zero.
Contribution
It establishes conditions under which the space of admissible metrics on such spaces is topologically equivalent to c0, extending understanding of metric spaces with the compact-open topology.
Findings
EM(X) is homeomorphic to c0 under specified conditions.
The space of admissible metrics has the topology of sequences converging to zero.
Provides a topological classification for metric spaces with certain connectedness properties.
Abstract
For a separable locally compact but not compact metrizable space , let be the one-point compactification with the point at infinity . We denote by the space consisting of admissible metrics on , which can be extended to an admissible metric on , endowed with the compact-open topology. Let be the space of sequences converging to . In this paper, we shall show that if is separable, locally connected and locally compact but not compact, and there exists a sequence of connected sets in such that for all positive integers with , , and for each compact set , there is a positive integer such that for any , , then is…
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Approximation Theory and Sequence Spaces
