- #1

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,784

- 18

whoopsies

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter quasar987
- Start date

- #1

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,784

- 18

whoopsies

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 964

quasar987 said:1. Homework Statement

According to the dfn, a subset A of a metric space is sequentially compact is every sequence in A has a subsequence that converges to a point in A.

An example of a sequentially compact set that comes to mind is R itself.

Then, Bolzano-Weierstrass's thm says that sequentially compactness and compactness are equivalent.

Finally, Heine-Borel's thm says that in R^n, compactness and closed+bounded are equivalent.

Thus, in R^n, closed+bounded and sequentially compactness are equivalent. But R is not bounded. What's going on?

Share: