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    Topological Spaces and Continuity

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    Let be a real valued function on a topological space .

    Show that is continuous if and only if for each real number the set and
    are open.

    Show that is continuous if and only if for each real number the set is
    open and is closed.

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    https://brainmass.com/math/geometry-and-topology/topological-spaces-continuity-164576

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    Topological spaces and continuity are investigated. The solution is detailed and well presented.

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