On metric spaces where continuous real valued functions are uniformly continuous in ZF
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: Topology and its Applications
سال: 2016
ISSN: 0166-8641
DOI: 10.1016/j.topol.2016.07.021