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Math Help - Prove they are connected sets

  1. #1
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    Prove they are connected sets

    Let A = {(0,y) in R^2 : y in R}
    Let B = {(x,y) in R^2 : (x-1)^2 + y^2 < 1}

    Is A connected?
    Is B connected?
    Is AUB connected?
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  2. #2
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    The set A is simply the y-axis.
    The set B is the interior of a disk centered at (1,0) with radius 1.
    Take note that (0,0) is a limit point of B as well as a point of A.
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