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 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
Originally Posted by cp05