Uniform Continuity on Compact Sets and Cauchy Sequences

[@armanavagyan1876]

Thanks PROF 👍

[@mikethemathematician]

Thanks a million @armanavagyan1876

[@sumittete2804]

Sir, If a function is uniformly continuous on a closed interval, could we refine the definition of uniform continuity by replacing the condition |x-y| < δ and |f(x) - f(y)| < ε with |x-y| ≤ δ implying |f(x) - f(y)| ≤ ε ?

[@angadbhatti123123]

But when convergence point is not in compact set non uniform function will also be continuous in compact set.....
I can say y = x^2 is continuous in compact set [1,5] so it should be uniform function....won't this be a contradiction to the theorm?

[@mikethemathematician]

@angadbhatti123123 good point! I was assuming throughout the video that E was a subset of the domain of f.