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November 23rd, 2015, 07:43 PM   #1
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Finding a continuous function and a sequentially compact K

I am looking for a function f: R-->R and a sequentially compact K subset of R such that the inverse f^-1(K) is not sequentially compact.

I decided to choose f(x) = sin(x), but I'm not sure what K could be such that f^-1(K) is not sequentially compact.

Are there any ideas about what K can be? I'm having a hard time grasping the concept of sequentially compact.
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