# If K is a compact, connected subset of R^2 and f: K-->R is a continuous function, what can you say about f(K)?

I only can deduce that f(K) is also connect and it is an interval. I feel like there is something more....perhaps uniform continuity?

### 2 Answers

- Mr. BrightsideLv 59 years agoFavorite Answer
Uniform continuity is something you may mention when you are asked about the function f(x).

Here, you are asked about f(K), which is a set.

You can deduce that f(K) is connected, true. The fact that it is an interval does not add any more information, since a connected set is also an interval...

The other thing you can deduce is that f(K) is compact, because a continuous function maps a compact set to a compact set.

- parkersLv 43 years ago
Oh my gosh, that's hilarious. I wasn't taking under consideration what the crucial become wondering, yet i realized after a lengthy time period that .... yeah. XD large funny tale; i prefer to inform this to someone! xD