MAST30026 Lecture 22: Urysohn's lemma

I gave the proof of Urysohn's lemma and briefly elaborated some of its important consequences. Given a pair of closed disjoint subsets of a normal topological space, the lemma asserts the existence of a real-valued continuous function on the space which takes the value 0 on the first closed subset and the value 1 on the other.

Have questions? I hold free public online office hours for this class, every week, all year. Drop in and say Hi! For details see the class webpage.

[wdacademia]

Thanks for posting this lecture series online. It's one of the best on youtube. I hope you add more in the future!

[markborz]

Isn't the second part of the proof obvious?
One can use A as starting point, then because of normality find an open U1 with A<U1 (subset), make closure, which is closed set, find U2 again because of normality and so on. This gives an infinite countable set, which can be mapped to the natural numbers and then to Q for enumeration of the open sets Ui.

[sanjursan]

Need a smooth ride from Medellin to Bogota? Easy, just use Urysohn's Llama.