ThmDex – An index of mathematical definitions, results, and conjectures.
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Zermelo-Fraenkel set theory
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Definition D2221
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}
Children
Countable set
Isomorphic sets
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 $\text{Bij}(X \to Y)$.