A function $f: X \to Y$ is said to be surjective if it covers its entire codomain $Y$. That is, $$ \forall y \in Y, \exists x \in X \mid f(x) = y $$ ...

This is a preview. Log in through your library . Abstract If $f: \mathbf{R}^m \rightarrow \mathbf{R}^m$ is continuous and locally injective, then f is in fact ...

Let $I = \lbrack 0, 1 \rbrack, \mathscr{B} =$ Lebesgue measurable subsets of [0, 1], and let $\lambda$ denote the Lebesgue measure on $(I, \mathscr{B})$. Let $\tau: I ...