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November 23rd, 2015, 08:43 PM  #1 
Newbie Joined: Nov 2015 From: Minneapolis Posts: 1 Thanks: 0  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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compact, continuous, finding, function, sequentially 
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