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(solution) Suppose X and X are both metric spaces, with metrics d x , d y


Suppose X and X are both metric spaces, with metrics dx, dy respectively. 

a) Show that XxY can be made into a metric space using the metric for all (x,y),(x2,y2) in XxY, d((x,y),(x2,y2))=dx(x1,x2) + dy(y1,y2)

b) Show that x + y can be made into a metric space via metric defined: d((x,y),(x2,y2))= (dx(x,x2)dy(y,y2))

 


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