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    Connected Set Topology on R^2 \ Q^2

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    Let S = R^2 Q^2. Points (x,y) in S have at least one irrational coordinate.

    Is S connected? Can we disprove with a counterexample?

    © BrainMass Inc. brainmass.com October 9, 2019, 8:24 pm ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/connected-set-topology-on-r-2-q-2-150059

    Solution Preview

    The answer is YES.
    Proof:
    We want to show that S is connected. This means for any two points A=(x1,y1) and B=(x2,y2) in S, we can find a
    path p in S, connecting A and B.
    For the point A=(x1,y1), without the loss of generality, we can assume that x1 is ...

    Solution Summary

    Connected Set Topology on R^2 Q^2 is investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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