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  3. euclidean metric) the metric d (( x 1 ,x 2 ) , ( y

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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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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