Non Compact set

Here I give an interesting example of a set that is closed and bounded, but not compact. So in some sense this is an infinite-dimensional counterexample to the Heine-Borel theorem.

[dougr.]

I always liked the quip “yo Momma’s so dumb she sits on the TV and watches the couch!”

[shivamchouhan]

0:01
Dr. Payam - Thanks for watching
Video ends

[jonatan]

When proving that the unit ball is closed, how do you conclude that |x_j|<=1 from the fact that |x^N_j| <=1? How can we guarantee that the inequality holds after taking the limit?

[homerwoods]

You can't take the t value of a set without first reexpressing it as a Hansen-Brögel subset and verifying it is σ-complete. Though in this case I suppose it works out fine.

[riadsouissi]

Can we also say (using similar proof) that the closed ball is not totally bounded ?

[SR-kdwi]

Is it worth pursuing phD in Math, if someone is not exceptionally talented?

[astronomer]

ولكن أنت لم تبين بأن F مجموعة مغلقة . إضافة إلى أن المنظم في حالة خاصة وليست عامة

[mathevengers]

How did they replied nine months before.