Proving Continuity of the Nearest Point function= Inf d(x,y) , y $in$ A , f:{$R^nto R$} (A is closed subset...
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This question already has an answer here:
Distance is (uniformly) continuous
2 answers
Prove that $f_A (x) = d({{x}}, A)$, is continuous.
2 answers
Let A be a non empty closed subset of $R^n$. $f:R^nto R$ by $f(x)= d(x,A)$ at each $xin R^n$ , where $d(x,A) = inf {d(x,y) , y in A}$.
Prove that $f$ is continuous on $R^n$.
It seems that it is true, but sets are not compact. I need some hints. Do you have any?
general-topology functions continuity metric-spaces
edited Nov 26 '18 at 19:52
Martin Sleziak
44.7k9117272
asked Nov 26 '18 at 17:47
EKarabulutEKarabulut
12
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marked as duplicate by José Carlos Santos, Aweygan, amWhy, Martin Sleziak, Davide Giraudo Nov 26 '18 at 21:55
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Distance is (uniformly) continuous
2 answers
Prove that $f_A (x) = d({{x}}, A)$, is continuous.
2 answers
Let A be a non empty closed subset of $R^n$. $f:R^nto R$ by $f(x)= d(x,A)$ at each $xin R^n$ , where $d(x,A) = inf {d(x,y) , y in A}$.
Prove that $f$ is continuous on $R^n$.
It seems that it is true, but sets are not compact. I need some hints. Do you have any?
general-topology functions continuity metric-spaces
edited Nov 26 '18 at 19:52
Martin Sleziak
44.7k9117272
asked Nov 26 '18 at 17:47
EKarabulutEKarabulut
12
$endgroup$
marked as duplicate by José Carlos Santos, Aweygan, amWhy, Martin Sleziak, Davide Giraudo Nov 26 '18 at 21:55
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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Use the inequality $|d(x,A)-d(y,A)|leq d(x,y)$
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– UserS
Nov 26 '18 at 17:49
add a comment |
$begingroup$
This question already has an answer here:
Distance is (uniformly) continuous
2 answers
Prove that $f_A (x) = d({{x}}, A)$, is continuous.
2 answers
Let A be a non empty closed subset of $R^n$. $f:R^nto R$ by $f(x)= d(x,A)$ at each $xin R^n$ , where $d(x,A) = inf {d(x,y) , y in A}$.
Prove that $f$ is continuous on $R^n$.
It seems that it is true, but sets are not compact. I need some hints. Do you have any?
general-topology functions continuity metric-spaces
edited Nov 26 '18 at 19:52
Martin Sleziak
44.7k9117272
asked Nov 26 '18 at 17:47
EKarabulutEKarabulut
12
$endgroup$
This question already has an answer here:
Distance is (uniformly) continuous
2 answers
Prove that $f_A (x) = d({{x}}, A)$, is continuous.
2 answers
Let A be a non empty closed subset of $R^n$. $f:R^nto R$ by $f(x)= d(x,A)$ at each $xin R^n$ , where $d(x,A) = inf {d(x,y) , y in A}$.
Prove that $f$ is continuous on $R^n$.
It seems that it is true, but sets are not compact. I need some hints. Do you have any?
This question already has an answer here:
Distance is (uniformly) continuous
2 answers
Prove that $f_A (x) = d({{x}}, A)$, is continuous.
2 answers
general-topology functions continuity metric-spaces
general-topology functions continuity metric-spaces
edited Nov 26 '18 at 19:52
Martin Sleziak
44.7k9117272
asked Nov 26 '18 at 17:47
EKarabulutEKarabulut
12
edited Nov 26 '18 at 19:52
Martin Sleziak
44.7k9117272
asked Nov 26 '18 at 17:47
EKarabulutEKarabulut
12
edited Nov 26 '18 at 19:52
Martin Sleziak
44.7k9117272
edited Nov 26 '18 at 19:52
Martin Sleziak
44.7k9117272
edited Nov 26 '18 at 19:52
Martin Sleziak
44.7k9117272
44.7k9117272
asked Nov 26 '18 at 17:47
EKarabulutEKarabulut
12
asked Nov 26 '18 at 17:47
EKarabulutEKarabulut
12
asked Nov 26 '18 at 17:47
EKarabulutEKarabulut
12
12
marked as duplicate by José Carlos Santos, Aweygan, amWhy, Martin Sleziak, Davide Giraudo Nov 26 '18 at 21:55
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by José Carlos Santos, Aweygan, amWhy, Martin Sleziak, Davide Giraudo Nov 26 '18 at 21:55
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
Use the inequality $|d(x,A)-d(y,A)|leq d(x,y)$
$endgroup$
– UserS
Nov 26 '18 at 17:49
add a comment |
$begingroup$
Use the inequality $|d(x,A)-d(y,A)|leq d(x,y)$
$endgroup$
– UserS
Nov 26 '18 at 17:49
$begingroup$
Use the inequality $|d(x,A)-d(y,A)|leq d(x,y)$
$endgroup$
– UserS
Nov 26 '18 at 17:49
$begingroup$
Use the inequality $|d(x,A)-d(y,A)|leq d(x,y)$
$endgroup$
– UserS
Nov 26 '18 at 17:49
add a comment |
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$begingroup$
Use the inequality $|d(x,A)-d(y,A)|leq d(x,y)$
$endgroup$
– UserS
Nov 26 '18 at 17:49