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Math Help - Topology. Metric Space.

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    Topology. Metric Space.

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    Re: Topology. Metric Space.

    Quote Originally Posted by vercammen View Post
    Picture attached.
    You have posted an attachment without any comment whatsoever.
    Do you expect someone to do the problem(s) for you?

    Each of these follows from this theorem:
    (\forall x,~y)\left[|D(A,x)-D(A,y)|\le d(x,y)\right]

    The proof follows directly from the definition: D(A,x)=\inf\{d(x,a):~a\in A\}~.

    Note that if \delta>0 then \exists b\in A such that D(A,x)\le d(x,b)<D(A,x)+\delta.

    Also note that \forall a\in A we know D(A,x)\le d(x,a).
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