![f: [a,b] to R be a continous function s.t. f(a)<c<f(b) then x belongs to (a,b) s.t. f(x) = c | Limit and Continuity | continuity and connectedness | Real Analysis](https://omgmaths.com/wp-content/uploads/2021/03/U1c3X62dBKs-maxresdefault-440x264.jpg)
Description
Every connected subset of R is an interval
The Real line R is connected
Every interval is connected
In R, intervals and only intervals are connected.
A subset E of R is connected iff E is an interval
Connected sets | connectedness | Theorem | Real Analysis | Metric Space | Topology | connectedness in Real Analysis | Point set topology