LIPSCHITZ FUNCTIONS OF ORDER ALPHA ARE UNIFORMLY CONTINUOUS

LIPSCHITZ FUNCTIONS ARE UNIFORMLY CONTINUOUS-PART 1 LINK:
• Lipschits functions ar...
f(x) = x^2 IS NOT UNIFORMLY CONTINUOUS ON R
PROOF: • CSIR NET 2014 JUNE B Q...

[@vidyutranjan]

Sir please continue uploading videos , you give detailed solution .

[@mathematicalworld5795]

Sir i saw one example without proof in the book metric spaces Q N ansari Let X be a discrete metric space and Y be any metric space then any function f:X--->Y is uniform countieous please explain how it is by example

[@HelloMathematicians]

Let epsilon>0 be given. We want delta such that |x-y|

[@mathematicalworld5795]

@@HelloMathematicians x and y are equal in domain which implies that |f(x) -f(y) |=0< Epsilon is it correct sir?

[@HelloMathematicians]

Yes. Correct. delta is independent of x and y. Therefore f is uniformly continuous. Note that, delta is independent of the epsilon also and any 0

[@amardeep4591]

Nice

[@HelloMathematicians]

Thanks :)