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mona123456

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problem in topologie

hello, please help me to sove this problem:
Let f be a finite function on Rn and define :
w(b)=sup{|f(x)-f(y)|:| x-y|< b}
b >0,to be the modulus of continuity of f.
show that w(b) decreases as b decreases to 0 and that f is uniformly continuous if and only if w(b) decrease to 0 as b decrease to 0