The techniques used in the proof helped me clarify some other topology properties, thank you so much 👍🏻

Excellent presentation of this theorem. Great idea to start with a metric space. 👍

Amazing video. Thank you so much!

Well done sir!

Thank you so much Prof.

Heine Borel Thm bring me here❤️❤️❤️

I'm hopelessly bad at math, but I love your videos anyway! :)

why bounded set is less or equal to, but not less than? It is clear that

subscribed just from that beautiful "subscribe" pointing

If we were in a general topological space and not necessarily a metric space, how would you define the notion of boundedness?

So simple and clean! I don't quite get why it's necessary when you're showing compact => closed, to choose a ball of radius 1/2n_1, rather than just 1/n_1. Wouldn't the ball of radius 1/n_1 be separated too if S is contained in S_{1/n_1}=compliment(closure(B_(1/n_1))), which has to be disjoint to B_(1/n_1)?

Really, the proof for compact implies closed goes much more smoothly if we use the Bolzano Weierstrass property.

6:28

this is how you prove ?