We present a notion of a finitely chainable subset of a metric space . We show that is a finitely chainable subset of if and only if is a bounded subset of for any uniformly locally Lipschitzian or uniformly continuous real-valued function on . As a corollary we reprove the Atsuji theorem in a slightly stronger form.
Cite this article
G. Marino, Grzegorz Lewicki, P. Pietramala, Finite Chainability, Locally Lipschitzian and Uniformly Continuous Functions. Z. Anal. Anwend. 17 (1998), no. 4, pp. 795–803