How would I go about proving a continuous function maps compact sets into compact sets for the reals? I have seen this question pointing me to the Intermediate Value Theorem wiki, but I am still confused. Other answers use topology terms and inverse images, but I don't have those defined yet in my course.

  • $\begingroup$ What's the concept of “compact” that you are working with? $\endgroup$ – José Carlos Santos Dec 18 '18 at 13:33


Start with an open cover of the image, then using the fact that the function is continuous shows the preimage of that cover is open and covers the domain (i.e the compact set), therefore it has an open subcover. It should follow easily from there

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