Problem

Source: Romania National Olympiad 2022

Tags: calculus, romania, function



Let $f:[0,1]\to(0,1)$ be a surjective function. Prove that $f$ has at least one point of discontinuity. Given that $f$ admits a limit in any point of the interval $[0,1],$ show that is has at least two points of discontinuity. Mihai Piticari and Sorin Rădulescu