Question

show that d is a metric on a map D(x,y):=2d(x,y)

Answer 1

i dont know about metric space but JamesJ does
i hope this help

Answer 2

what is D(x,y) ??

Answer 3

you can't define a metric by just just a function without any rule. you might have different rules that might not be metric.

Answer 4

you use the definition of a metric spaces together with their conditions,and they should all hold for it to be a metric space.