Continuity and Uniform Continuity
The function fis said to be uniformly continuous on Si 8">0 9 >0 8x 0 2S8x2S jx x 0j< =)jf(x) f(x 0)j<" : Hence fis not uniformly continuous on Si 9">0 8 >0 9x 0 2S9x2S jx x 0j< and jf(x) f(x 0)j " : 1For an example of a function which is not continuous see Example 22 below. 1. 4. The only di erence between the two de nitions is the order of ...
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