In the topology,dist(x,A)=d(x,y)
Giving the example of a set A ⊂ X and a point x ∈ X such that dist(x,A)=d(x,y) for :
1) all y ∈ A
2)a single point y ∈ A
3)exactly 3 points y ∈ A
Does anybody who someone to giving the example to over writing instances and draw pictures ?
Thanks a lot
metric-spaces
asked Nov 27 '18 at 21:01
arbade
13
add a comment |
Giving the example of a set A ⊂ X and a point x ∈ X such that dist(x,A)=d(x,y) for :
1) all y ∈ A
2)a single point y ∈ A
3)exactly 3 points y ∈ A
Does anybody who someone to giving the example to over writing instances and draw pictures ?
Thanks a lot
metric-spaces
asked Nov 27 '18 at 21:01
arbade
13
add a comment |
Giving the example of a set A ⊂ X and a point x ∈ X such that dist(x,A)=d(x,y) for :
1) all y ∈ A
2)a single point y ∈ A
3)exactly 3 points y ∈ A
Does anybody who someone to giving the example to over writing instances and draw pictures ?
Thanks a lot
metric-spaces
asked Nov 27 '18 at 21:01
arbade
13
Giving the example of a set A ⊂ X and a point x ∈ X such that dist(x,A)=d(x,y) for :
1) all y ∈ A
2)a single point y ∈ A
3)exactly 3 points y ∈ A
Does anybody who someone to giving the example to over writing instances and draw pictures ?
Thanks a lot
metric-spaces
metric-spaces
asked Nov 27 '18 at 21:01
arbade
13
asked Nov 27 '18 at 21:01
arbade
13
edited Nov 28 '18 at 0:20
asked Nov 27 '18 at 21:01
arbade
13
asked Nov 27 '18 at 21:01
arbade
13
asked Nov 27 '18 at 21:01
arbade
13
13
add a comment |
add a comment |
1 Answer
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We shall consider subsets of the plane $X=Bbb R^2$ endowed with the standard metric.
1) $A$ is a one-point set and $x$ is an arbitrary point or $A$ is a circle and $x$ is its center.
2) $A$ is a convex closed set (for instance, a disk or a straight line) and $x$ is an arbitrary point.
3) $A$ is a triangle and $x$ is the center of its incircle.
At the picture the point $x$ is red, the set $A$ is grey, and the subset of points of $A$ which are closest to $x$ is black.
answered Nov 27 '18 at 21:35
Alex Ravsky
39.2k32080
Could you giving the example for 1,2 and 3 like drawing a picture ?
– arbade
Nov 28 '18 at 0:12
1
Thank you so much!
– arbade
Nov 28 '18 at 9:02
add a comment |
Your Answer
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1 Answer
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1 Answer
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active
oldest
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votes
We shall consider subsets of the plane $X=Bbb R^2$ endowed with the standard metric.
1) $A$ is a one-point set and $x$ is an arbitrary point or $A$ is a circle and $x$ is its center.
2) $A$ is a convex closed set (for instance, a disk or a straight line) and $x$ is an arbitrary point.
3) $A$ is a triangle and $x$ is the center of its incircle.
At the picture the point $x$ is red, the set $A$ is grey, and the subset of points of $A$ which are closest to $x$ is black.
answered Nov 27 '18 at 21:35
Alex Ravsky
39.2k32080
Could you giving the example for 1,2 and 3 like drawing a picture ?
– arbade
Nov 28 '18 at 0:12
1
Thank you so much!
– arbade
Nov 28 '18 at 9:02
add a comment |
We shall consider subsets of the plane $X=Bbb R^2$ endowed with the standard metric.
1) $A$ is a one-point set and $x$ is an arbitrary point or $A$ is a circle and $x$ is its center.
2) $A$ is a convex closed set (for instance, a disk or a straight line) and $x$ is an arbitrary point.
3) $A$ is a triangle and $x$ is the center of its incircle.
At the picture the point $x$ is red, the set $A$ is grey, and the subset of points of $A$ which are closest to $x$ is black.
answered Nov 27 '18 at 21:35
Alex Ravsky
39.2k32080
Could you giving the example for 1,2 and 3 like drawing a picture ?
– arbade
Nov 28 '18 at 0:12
1
Thank you so much!
– arbade
Nov 28 '18 at 9:02
add a comment |
We shall consider subsets of the plane $X=Bbb R^2$ endowed with the standard metric.
1) $A$ is a one-point set and $x$ is an arbitrary point or $A$ is a circle and $x$ is its center.
2) $A$ is a convex closed set (for instance, a disk or a straight line) and $x$ is an arbitrary point.
3) $A$ is a triangle and $x$ is the center of its incircle.
At the picture the point $x$ is red, the set $A$ is grey, and the subset of points of $A$ which are closest to $x$ is black.
answered Nov 27 '18 at 21:35
Alex Ravsky
39.2k32080
We shall consider subsets of the plane $X=Bbb R^2$ endowed with the standard metric.
1) $A$ is a one-point set and $x$ is an arbitrary point or $A$ is a circle and $x$ is its center.
2) $A$ is a convex closed set (for instance, a disk or a straight line) and $x$ is an arbitrary point.
3) $A$ is a triangle and $x$ is the center of its incircle.
At the picture the point $x$ is red, the set $A$ is grey, and the subset of points of $A$ which are closest to $x$ is black.
answered Nov 27 '18 at 21:35
Alex Ravsky
39.2k32080
edited Nov 28 '18 at 2:09
answered Nov 27 '18 at 21:35
Alex Ravsky
39.2k32080
answered Nov 27 '18 at 21:35
Alex Ravsky
39.2k32080
answered Nov 27 '18 at 21:35
Alex Ravsky
39.2k32080
39.2k32080
Could you giving the example for 1,2 and 3 like drawing a picture ?
– arbade
Nov 28 '18 at 0:12
1
Thank you so much!
– arbade
Nov 28 '18 at 9:02
add a comment |
Could you giving the example for 1,2 and 3 like drawing a picture ?
– arbade
Nov 28 '18 at 0:12
1
Thank you so much!
– arbade
Nov 28 '18 at 9:02
Could you giving the example for 1,2 and 3 like drawing a picture ?
– arbade
Nov 28 '18 at 0:12
Could you giving the example for 1,2 and 3 like drawing a picture ?
– arbade
Nov 28 '18 at 0:12
1
1
Thank you so much!
– arbade
Nov 28 '18 at 9:02
Thank you so much!
– arbade
Nov 28 '18 at 9:02
add a comment |
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