Let M be a subspace of a complete metric space X and suppose all continuous real valued functions on M are...
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Let M be a subspace of a complete metric space X and suppose all continuous real valued functions on M are uniformly continuous functions. The problem is to prove that M is compact. How can I start solving this problem?
functional-analysis
asked Dec 23 '18 at 8:35
Gera SlanovaGera Slanova
503
$endgroup$
add a comment |
$begingroup$
Let M be a subspace of a complete metric space X and suppose all continuous real valued functions on M are uniformly continuous functions. The problem is to prove that M is compact. How can I start solving this problem?
functional-analysis
asked Dec 23 '18 at 8:35
Gera SlanovaGera Slanova
503
$endgroup$
$begingroup$
I think you need to assume $M$ is connected, see PhoemueX's comment in math.stackexchange.com/questions/2202362/…
$endgroup$
– Alex Vong
Dec 23 '18 at 9:05
add a comment |
$begingroup$
Let M be a subspace of a complete metric space X and suppose all continuous real valued functions on M are uniformly continuous functions. The problem is to prove that M is compact. How can I start solving this problem?
functional-analysis
asked Dec 23 '18 at 8:35
Gera SlanovaGera Slanova
503
$endgroup$
Let M be a subspace of a complete metric space X and suppose all continuous real valued functions on M are uniformly continuous functions. The problem is to prove that M is compact. How can I start solving this problem?
functional-analysis
functional-analysis
asked Dec 23 '18 at 8:35
Gera SlanovaGera Slanova
503
asked Dec 23 '18 at 8:35
Gera SlanovaGera Slanova
503
asked Dec 23 '18 at 8:35
Gera SlanovaGera Slanova
503
asked Dec 23 '18 at 8:35
Gera SlanovaGera Slanova
503
asked Dec 23 '18 at 8:35
Gera SlanovaGera Slanova
503
503
$begingroup$
I think you need to assume $M$ is connected, see PhoemueX's comment in math.stackexchange.com/questions/2202362/…
$endgroup$
– Alex Vong
Dec 23 '18 at 9:05
add a comment |
$begingroup$
I think you need to assume $M$ is connected, see PhoemueX's comment in math.stackexchange.com/questions/2202362/…
$endgroup$
– Alex Vong
Dec 23 '18 at 9:05
$begingroup$
I think you need to assume $M$ is connected, see PhoemueX's comment in math.stackexchange.com/questions/2202362/…
$endgroup$
– Alex Vong
Dec 23 '18 at 9:05
$begingroup$
I think you need to assume $M$ is connected, see PhoemueX's comment in math.stackexchange.com/questions/2202362/…
$endgroup$
– Alex Vong
Dec 23 '18 at 9:05
add a comment |
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$begingroup$
I think you need to assume $M$ is connected, see PhoemueX's comment in math.stackexchange.com/questions/2202362/…
$endgroup$
– Alex Vong
Dec 23 '18 at 9:05