Set of bijections – TheoremDex

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Set of bijections

Formulation 1

Let $X$ and $Y$ each be a D11: Set.
The set of bijections from $X$ to $Y$ is the D11: Set \begin{equation} \text{Bij}(X \to Y) : = \{ f \mid f : X \to Y \text{ is a bijection} \} \end{equation}

Conventions

Convention 0 (Notation for set of bijections) : Let $X$ and $Y$ each be a D11: Set. We denote the D2221: Set of bijections from $X$ to $Y$ by $\text{Bij}(X \to Y)$.

Child definitions

» D16: Countable set
» D1523: Isomorphic sets

Results

» R2914: Cantor-Bernstein theorem