Atsuji completions vis-á-vis hyperspaces

Year, pages: 2008, 497 - 508

A metric space $(X,d)$ is called an Atsuji space if every real-valued continuous function on $(X,d)$ is uniformly continuous. It is well-known that an Atsuji space must be complete. A metric space $(X,d)$ is said to have an Atsuji completion if its completion $(\hat{X},d)$ is an Atsuji space. In this paper, we study twelve equivalent (external) characterizations for a metric space to have an Atsuji completion in terms of hyperspace topologies. We also characterize topologically those metrizable spaces whose completions are Atsuji spaces.

Jain, T., Kundu, S. 2008. Atsuji completions vis-á-vis hyperspaces. In Mathematica Slovaca, vol. 58, no.4, pp. 497-508. 0139-9918.

Jain, T., Kundu, S. (2008). Atsuji completions vis-á-vis hyperspaces. Mathematica Slovaca, 58(4), 497-508. 0139-9918.