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Hello! How to prove the min function is continuous?

  1. Oct 27, 2008 #1

    Could anybody give me an idea about this proof?

    knowing [tex]f_{i}:X\rightarrow[/tex]R i=1,2

    to show whether [tex]f_{3}=min{f_{1},f_{2}}[/tex] is continuous!

    Thanks in advance,

  2. jcsd
  3. Oct 27, 2008 #2


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    Presumably f1 and f2 are continuous themselves? Is this a homework problem? I'll give you a small hint: work on the points where f1(x)=/=f2(x) and f1(x)=f2(x) separately
  4. Oct 27, 2008 #3
    yeah, thanks, a lot, I finally find that it is convenient to construct it using the gluing lemma.
  5. Oct 29, 2008 #4
    quick solution:

    min(f, g) = (f+g)/2 - |f-g|/2
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