Recent content by scottyg88

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    Convergence of Sequences and closed sets

    I see! Quite an oversight on my part... thanks for the help!
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    Convergence of Sequences and closed sets

    Does the statement not also imply that a subset containing a convergent sequence AND its limit must be a CLOSED subset in the metric space? This is the part I have a question about. Why could a subset contain a convergent sequence and its limit, but be an OPEN subset? Thanks in advanced for...
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    Convergence of Sequences and closed sets

    Homework Statement This is the Theorem as stated in the book: Let S be a subset of a metric space E. Then S is closed if and only if, whenever p1, p2, p3,... is a sequence of points of S that is convergent in E, we have: lim(n->inf)pn is in S. Homework Equations From "introduction to...