if we know that f : [a,b] ----> reals is continuous. How can we prove that the image f([a,b]) is a closed interval say [m,M] for some m,M in reals?

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- February 4th 2011, 05:40 AMmaximus101Analysis question no.2
if we know that f : [a,b] ----> reals is continuous. How can we prove that the image f([a,b]) is a closed interval say [m,M] for some m,M in reals?

- February 4th 2011, 05:43 AMHallsofIvy
A continuous function maps a compact set to a compact set.

- February 4th 2011, 07:35 AMtonio