? asked in Science & MathematicsMathematics · 9 years ago

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

  • 9 years ago
    Favorite 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.

  • 3 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

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