# Math Help - compact connected

1. ## 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.

2. Originally Posted by cp05
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 $[a,b]$