- #1
Euge
Gold Member
MHB
POTW Director
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Here is this week's POTW:
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Prove that the quotient of a Banach space $X$ by a closed linear subspace $M$ is Banach with respect to the norm $$\|x + M\| := \inf\{\|x + y\|_X : y\in M\}\quad (x\in X)$$
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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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Prove that the quotient of a Banach space $X$ by a closed linear subspace $M$ is Banach with respect to the norm $$\|x + M\| := \inf\{\|x + y\|_X : y\in M\}\quad (x\in X)$$
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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!