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Math Help - Topology (1)

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    Topology (1)

    Let (E,d) be a metric space.
    Show that the function d'(x,y) = d(x,y)/1 + (d(x,y)) is a metric on E topologically equivalent to d.
    Is it metrically equivalent to d'?

    Thanks
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    Quote Originally Posted by taypez View Post
    Let (E,d) be a metric space.
    Show that the function d'(x,y) = d(x,y)/1 + (d(x,y)) is a metric on E topologically equivalent to d.
    Is it metrically equivalent to d'?

    Thanks
    Perhaps I'm just in a caustic mood this morning, but how can you possibly be studying topology and write
    "d(x, y)/1 + d(x, y)" to mean \frac{d(x, y)}{1 + d(x, y)}??

    This should be written "d(x, y)/(1 + d(x, y))."

    -Dan
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