- #1
Euge
Gold Member
MHB
POTW Director
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- 244
Here is this week's POTW:
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Consider a sequence $f_n : M\to M'$ between two metric spaces $M$ and $M'$, where $n = 1,2,3,\ldots$. Prove that if each $f_n$ is bounded and $f_n$ converges uniformly to $f$, then $f$ is bounded.
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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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Consider a sequence $f_n : M\to M'$ between two metric spaces $M$ and $M'$, where $n = 1,2,3,\ldots$. Prove that if each $f_n$ is bounded and $f_n$ converges uniformly to $f$, then $f$ is bounded.
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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!