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    Solve: Topology Induced

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    Question: Find the interior, the closure, the accumulation points, the isolated point and the boundary points of the following sets.

    a) X = [(0,1) in R with the topology induced by d(x,y) = |x-y|]
    b) X = Q in R with the same topology as above.
    c) X = {(x,y) : |y| < x^2} U {(0,y), y E R} in R^2, with the topology induced by the norm || (x,y) || = max {|x|, |y|}.
    d) Same as in c), but the topology is now generated by the distance d ((x,y), (x_1,y_1)) = |x - x_1| + max {|y|, |y_1|}

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    https://brainmass.com/math/geometry-and-topology/topology-induced-369762

    Solution Summary

    This solution provides a detailed, step-wise response in which a topology induced inquiry is clearly modeled. The response is enclosed within an attached Word document.

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