1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Inverse image and continuity

  1. Apr 1, 2008 #1
    1. a) Show that (f^-1 S)compliment = f^-1(S compliment) for any set S of reals.

    Then use part a) to show The function f is continuous iff f^-1(S) is closed for every closed set S.

    2. inverse image = f^-1(S) = {x: f(x) [tex]\in[/tex] S}
    f is continous iff for every open set U [tex]\in[/tex] the reals, f^-1(U) is open.
  2. jcsd
  3. Apr 1, 2008 #2
    part a is true for any set, so you need to show f^-1(S^c) = (f^-1(S))^c,

    so take x in f^-1(S^c), so f(x) is in S^c, so f(x) is not in S, so ...

    for part b, what have you tried and what is your definition of continuous, delta/epsilon?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook