- #1

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It's been proven that totally bounded→bounded, so this is wrong. Why?

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- Thread starter johnqwertyful
- Start date

- #1

- 395

- 14

It's been proven that totally bounded→bounded, so this is wrong. Why?

- #2

- 395

- 14

in this proof of totally bounded implies bounded, he takes the maximum of d(xi,x1), which he assumes to be finite. So if we assume that the distance between every two points is finite, then we get totally bounded implies bounded.

- #3

jgens

Gold Member

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So if we assume that the distance between every two points is finite

This "assumption" is incorporated into the definition of metrics.

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