Homeomorphism between metric spaces
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How can I prove that every metric space is uniformly homeomorphic to a bounded metric space? I tried to prove this by using uniform continuity of the bijective function $f: X to L([a,b])$ and uniform continuity of its inverse but I don't know if this method is appropriate.
metric-spaces
asked Jan 8 at 16:58
user632059user632059
31
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add a comment |
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How can I prove that every metric space is uniformly homeomorphic to a bounded metric space? I tried to prove this by using uniform continuity of the bijective function $f: X to L([a,b])$ and uniform continuity of its inverse but I don't know if this method is appropriate.
metric-spaces
asked Jan 8 at 16:58
user632059user632059
31
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Duplicate of math.stackexchange.com/q/3065964.
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– Paul Frost
Jan 8 at 20:09
add a comment |
$begingroup$
How can I prove that every metric space is uniformly homeomorphic to a bounded metric space? I tried to prove this by using uniform continuity of the bijective function $f: X to L([a,b])$ and uniform continuity of its inverse but I don't know if this method is appropriate.
metric-spaces
asked Jan 8 at 16:58
user632059user632059
31
$endgroup$
How can I prove that every metric space is uniformly homeomorphic to a bounded metric space? I tried to prove this by using uniform continuity of the bijective function $f: X to L([a,b])$ and uniform continuity of its inverse but I don't know if this method is appropriate.
metric-spaces
metric-spaces
asked Jan 8 at 16:58
user632059user632059
31
asked Jan 8 at 16:58
user632059user632059
31
asked Jan 8 at 16:58
user632059user632059
31
asked Jan 8 at 16:58
user632059user632059
31
asked Jan 8 at 16:58
user632059user632059
31
31
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Duplicate of math.stackexchange.com/q/3065964.
$endgroup$
– Paul Frost
Jan 8 at 20:09
add a comment |
$begingroup$
Duplicate of math.stackexchange.com/q/3065964.
$endgroup$
– Paul Frost
Jan 8 at 20:09
$begingroup$
Duplicate of math.stackexchange.com/q/3065964.
$endgroup$
– Paul Frost
Jan 8 at 20:09
$begingroup$
Duplicate of math.stackexchange.com/q/3065964.
$endgroup$
– Paul Frost
Jan 8 at 20:09
add a comment |
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$begingroup$
Duplicate of math.stackexchange.com/q/3065964.
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– Paul Frost
Jan 8 at 20:09