Abstract:A metric space $\delimiter "426830A X,d\delimiter "526930B $ 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.
Keywords: $\operatorname {UC}$ space, boundedly $\operatorname {UC}$ space, boundedly compact space, Atsuji space, uniform continuity on bounded set{bounded set}s, topology of uniform convergence on bounded set{bounded set}s, Attouch--Wets topology
AMS Subject Classification: Primary 54E45; Secondary 54B20, 54C35