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Topology

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Functions Of Two Metrics

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Let $d_1$ and $d_2$ be two metrics on $X$.

Which of the following functions MUST also be metrics on $X$?

A

$d:=d_1 + d_2$.

B

$d:=d_1 - d_2$.

C

$d:=\max\{d_1, d_2\}$.

D

$d:=d_1\cdot d_2$.

E

$d:=d_1 + d_2/2$.

F

$d:=\max\{d_1/4, d_2\}$.