Geodesic
A generalization of boundedly compact metric spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 361-367.

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A metric space $\langle X,d\rangle$ is called a $\operatorname{UC}$ space provided each continuous function on $X$ into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that $\operatorname{UC}$ spaces play relative to the compact metric spaces.
Classification : 54B20, 54C35, 54E15, 54E45
Keywords: $\operatorname{UC}$ space; boundedly $\operatorname{UC}$ space; boundedly compact space; Atsuji space; uniform continuity on bounded sets; topology of uniform convergence on bounded sets; Attouch--Wets topology 
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     title = {A generalization of boundedly compact metric spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {361--367},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {1991},
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     zbl = {0766.54028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a17/}
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Beer, Gerald; Di Concilio, Anna. A generalization of boundedly compact metric spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 361-367. http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a17/