JournalszaaVol. 17, No. 4pp. 795–803

Finite Chainability, Locally Lipschitzian and Uniformly Continuous Functions

  • G. Marino

    Università della Calabria, Arcavacata Di Rende, Italy
  • Grzegorz Lewicki

    Jagiellonian University, Krakow, Poland
  • P. Pietramala

    Università della Calabria, Arcavacata di Rende, Italy
Finite Chainability, Locally Lipschitzian and Uniformly Continuous Functions cover
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Abstract

We present a notion of a finitely chainable subset of a metric space XX. We show that YY is a finitely chainable subset of XX if and only if f(Y)f(Y) is a bounded subset of R\mathbb R for any uniformly locally Lipschitzian or uniformly continuous real-valued function ff on XX. 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

DOI 10.4171/ZAA/850