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Math Help - examples of covers

  1. #1
    Junior Member
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    73

    examples of covers

    1) Show that each subset of R is not compact by describing an open cover for it that has no finite subcover.
    a) [1,3)
    b) N
    c) {x is and element of Q: 0 <= x <= 2}

    2)
    If S1 and S2 are compact subsets of R, prove that S1 U S2 is compact

    3) Find an uncountable open cover F of R such that F has no finite subcover. Does F contain a countable subcover?


    Here is what I have for problem one,let me know what you think.

    1)
    For (a) On = (.9, 3 - (1/n))

    For (b) On = (n - (1/4), n + 1/4)

    not sure on the rest
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  2. #2
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    When I say cover F, I mean script F
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