Injectiveness, surjectiveness, biuniqueness. Countability and uncountability of sets
Example
— biuniqueness, inverse mapping y = arcsin x.
Example
X = [−1; 1], Y = [0; 1], f(x) = x2 — surjection.
Example
X = [0; 1], Y = [0; 1], f(x) = x2 — injection, inverse mapping