The question comes from the Munkres text, p. 133 #3.
Let Xn be a metric space with metric dn, for n ε Z+.
Part (a) defines a metric by the equation
ρ(x,y)=max{d1(x,y),...,dn(x,y)}.
Then, the problem askes to show that ρ is a metric for the product space X1 x ... x Xn.
When I originally...