Recent content by ideas

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    Standard topology and discrete topology

    How to compare the topology on R generated by the subbasis S={[x,y)|x,y are rational}U{(x,y]|x,y rational} to the discrete topology on R?
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    How Does the Maximum Metric Define Topology on the Product of Two Metric Spaces?

    Homework Statement [/b] Let (X, dX ) and (Y , dY ) be metric spaces. The product of X and Y (written X × Y ) is the set of pairs {(x, y) : x ∈ X, y ∈ Y } with the metric: d((x1 , y1 ), (x2 , y2 )) = max {dX (x1 , x2 ), dY (y1 , y2 )} 1)How to prove that d is a metric on X × Y? 2)Prove that d...
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    Graduate Is the Maximum Metric Valid for Product Topology on Combined Metric Spaces?

    Let (X, dX ) and (Y , dY ) be metric spaces. The product of X and Y (written X × Y ) is the set of pairs {(x, y) : x ∈ X, y ∈ Y } with the metric: d((x1 , y1 ), (x2 , y2 )) = max {dX (x1 , x2 ), dY (y1 , y2 )} 1)How to prove that d is a metric on X × Y? 2)Prove that d induces the product...