Form equivalence class Howard-Rubin Number: 1

Statement:

Assume \(f: S\rightarrow R\) where \(R\subseteq S\). Then the retractions of \(S\) onto \(R\) (that is, the mappings \(g: S \rightarrow R\) which are the identity on \(R\)) are precisely the mappings \(f\circ h\) where \(h: S \rightarrow S\) and \((\forall y\in R)(h(y)\in f^{-1}(\{y\}))\).

Howard-Rubin number: 1 AC

Citations (articles): Smith [1982] Three propositions equivalent to the axiom of choice

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