# set theory/ topology question

by yxgao
Tags: theory or, topology
 P: 125 Let f be a real-valued function defined and continuous on the set of real numbers R. Which of the following must be true of the set S = {f(c): 0
 Sci Advisor HW Helper P: 9,398 it is bounded because it is continuous on the compact set [0,1] and the continuous image of a compact (closed and bounded set) is closed and bounded, the image of (0,1) is a subsert of this bounnded set and is hence bounded. define f(x) = 0 for all x. the image of an open set is then closed.
 P: 125 How can you reach a conclusion by simply considering the case f(x) = 0?
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