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Math Help - compact connected

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    compact connected

    What are compact connected sets in R?? I know compact is closed and bdd in R (and also that any sequence in R has a convergent subsequence), and connected means xn->x, then f(xn)->f(x), so would compact connected sets in R mean that for any xnk->x, f(xnk)->f(x)?? This question is really weird.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by cp05 View Post
    What are compact connected sets in R?? I know compact is closed and bdd in R (and also that any sequence in R has a convergent subsequence), and connected means xn->x, then f(xn)->f(x), so would compact connected sets in R mean that for any xnk->x, f(xnk)->f(x)?? This question is really weird.
    The only connected sets in \mathbb{R} are intervals and the compact sets are the closed and bounded ones. So, the only compact connected sets are closed and bounded intervals, i.e. intervals of the form [a,b]
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