On semicontinuity points (Q1061877)

For a real function f let C(f) be the set of all continuity points of f, \(S(f)(S^ 1(f))\) be the set of all upper (lower) semicontinuity points of f and \(T(f)(T^ 1(f))\) be the set of all points \(x\in R\), at which \[ f(x)> \limsup_{t\to x}f(t)\quad (f(x)<\lim \inf_{t\to x}f(t)). \] The necessary and sufficient conditions for five sets to be equal to the sets \(C(f),S(f),S^ 1(f),T(f)\) and \(T^ 1(f)\) (respectively) for some f are given.