Question

hi.help plz with metric spaces.

Answer 1

Where is the question?

Answer 2

oh still typing it

Answer 3

Prove that if \[(X _{i},d _{i}), 1 \le i \le n, \] is a finite family of metric spaces then d, given by \[d(x,y) = \sum_{i=1}^{n} d _{i}(x _{i},y _{i}),\] is a metric on \[X = \prod_{i=1}^{n}X _{i} = X _{1} \times X _{2} \times X _{3} \times ... \times X _{n}\]

Answer 4

What are \( X_i \) 's ... an interval or set??

Answer 5

X is a set

Answer 6

this does not look that hard ... where are you stuck??

Answer 7

it is the product of Xi's

Answer 8

do i have to use the definition of the set X or do i jst show that d is a metric

Answer 9

yes ... each Xi is a vector space. X will also be a vector space like this