Remarks and Solutions for Homework for Page 13
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#8. Let G be an open subset of X and consider Y \intersection G. Note that
    it is possible for some points of G to be in X and not in Y \inter. G.
    But that is ok in proving Y \inter. G open since the m.s. in this case
    is (Y, d) and not (X,d). The converse is based on the same concept. Let
    G be the smallest open subset of X that contains G_1. Prove that there
    is always such an open set in X.
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