1. Not finding help here? Sign up for a free 30min 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!

Analysis -Continuous Functions

  1. Nov 16, 2008 #1
    thanks I think I got it :)
    Last edited: Nov 16, 2008
  2. jcsd
  3. Nov 16, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    What you need is that if A is connected and f is continuous, then f(A) is connected, since the only connected sets in R are the intervals. "Compact" and bounded won't help since there is no requirement here that the interval be bounded. And knowing something is a subset of [a, b] doesn't tell you anything about that "something" being an interval!

    I think you need to use the "intermediate value" property of continous functions: If y is any number between f(a) and f(b), then there exist c in [a, b] such that f(c)= y.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Analysis -Continuous Functions
  1. Functional analysis (Replies: 5)

  2. Functional analysis (Replies: 1)