Finite Chainability, Locally Lipschitzian and Uniformly Continuous Functions
Copyright policy )Finite Chainability, Locally Lipschitzian and Uniformly Continuous Functions
We present a notion of a finitely chainable subset of a metric space X . We show that Y is a finitely chainable subset of X if and only if f(Y) is a bounded subset of \mathbb R for any uniformly locally Lipschitzian or uniformly continuous real-valued function f on X . As a corollary we reprove the Atsuji theorem in a slightly stronger form.
- Jagiellonian University Poland
- University of Calabria Italy
uniformly continuous function, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, Real-valued functions in general topology, metric space, Continuous maps, uniformly locally Lipschitzian function, finite chainable subset
uniformly continuous function, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, Real-valued functions in general topology, metric space, Continuous maps, uniformly locally Lipschitzian function, finite chainable subset
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