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.
@article{116977, author = {Gerald Beer and Anna Di Concilio}, title = {A generalization of boundedly compact metric spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {32}, year = {1991}, pages = {361-367}, zbl = {0766.54028}, mrnumber = {1137797}, language = {en}, url = {http://dml.mathdoc.fr/item/116977} }
Beer, Gerald; Di Concilio, Anna. A generalization of boundedly compact metric spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 361-367. http://gdmltest.u-ga.fr/item/116977/
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