- #1
Euge
Gold Member
MHB
POTW Director
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Here is this week's POTW:
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Prove that if $M$ is a metric space, then $M$ is finite if and only if the set $BC(M)$ of bounded continuous functions $f : M \to \Bbb R$ is a finite dimensional real vector space.-----
Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!
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Prove that if $M$ is a metric space, then $M$ is finite if and only if the set $BC(M)$ of bounded continuous functions $f : M \to \Bbb R$ is a finite dimensional real vector space.-----
Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!