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Math Help - Open set

  1. #1
    Member kezman's Avatar
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    Open set

    Let S Connected subset of R^2 and p \in R^2 accumulation point. Show that {p} union S is conected. What happends if p isnt a acummulation point?
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  2. #2
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    Proofs on connected sets depend on the sequence of text material you have.
    Look for a theorem about the existence of two disjoint open sets that separate \{ p \}\cup S.
    Note any open set that contains p must contain another point of S.
    But would that separate S?
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