Euclidean metric) The metric d (( x 1 ,x 2 ) , ( y 1 ,y 2 )) = ? ( x 1 ? x 2 ) 2 + ( y 1 ? y 2 ) 2 on R 2 generates the standard (product) topology on R 2 .

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Question

Advance Math

Euclidean metric) The metric
d
((
x
1
,x
2
)
,
(
y
1
,y
2
)) =
?
(
x
1
?
x
2
)
2
+ (
y
1
?
y
2
)
2
on
R
2
generates the standard (product) topology on
R
2
.

Answer & Explanation Solved by verified expert

4.1 Ratings (631 Votes)

The given metric isFirst we prove that the metric topology is contained in theproduct topology on Let be a point in and be an open set of metric topology See Answer

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Euclidean metric) The metric d (( x 1 ,x 2 ) , ( y 1 ,y 2 )) = ? ( x 1 ? x 2 ) 2 + ( y 1 ? y 2 ) 2 on R 2 generates the standard (product) topology on R 2 .

70.2K

Verified Solution

Question

Advance Math

Euclidean metric) The metric
d
((
x
1
,x
2
)
,
(
y
1
,y
2
)) =
?
(
x
1
?
x
2
)
2
+ (
y
1
?
y
2
)
2
on
R
2
generates the standard (product) topology on
R
2
.

Answer & Explanation Solved by verified expert

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Euclidean metric) The metric d (( x 1 ,x 2 ) , ( y 1 ,y 2 )) = ? ( x 1 ? x 2 ) 2 + ( y 1 ? y 2 ) 2 on R 2 generates the standard (product) topology on R 2 .

70.2K

Verified Solution

Question

Advance Math

Euclidean metric) The metricd((x1,x2),(y1,y2)) =?(x1?x2)2+ (y1?y2)2onR2generates the standard (product) topology onR2.

Answer & Explanation Solved by verified expert

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Other questions asked by students

Euclidean metric) The metric
d
((
x
1
,x
2
)
,
(
y
1
,y
2
)) =
?
(
x
1
?
x
2
)
2
+ (
y
1
?
y
2
)
2
on
R
2
generates the standard (product) topology on
R
2
.