What is uniform continuity?Give examples.
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In mathematics, a function f is uniformly continuous if, roughly speaking, it is possible to guarantee that f(x) and f(y) be as close to each other as we please by requiring only that x and y are sufficiently close to each other; unlike ordinary continuity, where the maximum distance between f(x) and f(y) may depend on x and y themselves.
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In particular, every function which is differentiable and has bounded derivative is uniformly continuous. More generally, every Hölder continuous function is uniformly continuous. Every member of a uniformly equicontinuous set of functions is uniformly continuous.
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