Topology Proceedings 30 No. 1 (2006), pp. 301-325

Atsuji Spaces: Equivalent Conditions

S. Kundu and Tanvi Jain

A metric space (X, d) is called an Atsuji space if every real-valued continuous function on (X, d) is uniformly continuous. In this paper, we study twenty-five equivalent conditions for a metric space to be an Atsuji space. These conditions have been collected from the works of several mathematicians spanning nearly four decades.

Keywords: accumulation point, asymptotic sequence, Atsuji space, compact, pseudo-Cauchy, uniform continuity

Mathematics Subject Classification: 5402 54C05 54E35 54E40 54E45 54E99

Document formats: PDF file 250.3 Kb

Topology Proceedings, Volume 30, No. 1 (2006)
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