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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Deepak singh 1 Best Answer
1. 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 be 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. 2. uniform continuity is a property of a function on a set whereas function is defined on single point . 3.Uniform continuity implies continuity . Uniform continuity is stronger notion of continuity . that's why uniform continuity is important.
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