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    Open subsets above and below f(x), proving continuity of f(x)

    Homework Statement Let f:R-->R be a function. Define A={(x,y) \in R2: y<f(x)}, B={(x,y) \in R2: y>f(x)}, i.e A is the subset of R2 under the graph of f and B is the subset above the graph of f. Show that if A and B are open subsets of R2, then f is continuous Homework Equations N/A...