On maximal groups of isometries
Abstract: The purpose of this note is to introduce the concept of ``Optimal Metrization'' for metrizable topological spaces. Let be such a space, a metric on and the group of all those homeomorphisms of onto itself which preserve . The metric is said to be ``optimal'' provided there is no with properly containing . A space having at least one optimal metric is called ``optimally metrizable.'' Examples of spaces which are and which are not optimally metrizable are given; it is shown that the real line is, and that the usual metric is optimal.
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Keywords: Group of isometries, optimal metric, optimally metrizable
Article copyright: © Copyright 1971 American Mathematical Society