Metric Spaces on which Continuous Functions are Uniformly Continuous and Hausdorff Distance
نویسندگان
چکیده
منابع مشابه
Metric Spaces on Which Continuous Functions Are Uniformly Continuous and Hausdorff Distance
Atsuji has internally characterized those metric spaces X for which each real-valued continuous function on X is uniformly continuous as follows: (1) the set X' of limit points of X is compact, and (2) for each £ > 0, the set of points in X whose distance from X' exceeds e is uniformly discrete. We obtain these new characterizations: (a) for each metric space V, the Hausdorff metric on C(X, Y),...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1985
ISSN: 0002-9939
DOI: 10.2307/2045860