Let f : Rn → R be convex with dom(f) = Ω ⊂ Rn an open set. Show that f is a continuous function on Ω

3. Is there a function f: R² → R that is not continuous but f(U) is open in R for all open sets UC R²?

Give an example of a bounded function that is defined on R, continuous at each point except the points 1 and-1, and has neither a removable discontinuity nor a jump discontinuity at 1 and-1.

Let f : [a, b] → R be a strictly decreasing function. Prove that f is integrable [a, b). on