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?
- 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
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