402.4Y7 Continuous Extension to Compact Domain is Uniformly Continuous

0:00 Introduction
1:19 Is This Uniformly Continuous on (0,1)?
2:39 The Extension Plan
2:58 Fill In the "Holes" at the Endpoints...
4:09 ...To Get a "Larger" Continuous Function.
5:05 The Larger Function is Uniformly Continuous...
5:56 ...So the Original Function Is Too.
6:38 Wrapup

[abdonecbishop]

kind of looks like analytical continuation...well done

[duckymomo]

How can we conclude that sqrt(x), from 0 to infinity, is uniformly continuous?

a) it’s not lipschitz
b) it’s not in a compact domain
c) it can’t be extended into compact either