Form equivalence class Howard-Rubin Number: 1

Statement:

Assume \(f: S \rightarrow R\) where \(f\) is surjective and \(R\subseteq S\).Then the mappings of \(S\) onto \(R\) are precisely the mappings of the form \(f\circ h\)  where \(h: S\rightarrow S\) and \((\forall y\in R)(\exists x\in S)(h(x)\in f^{-1}(\{y\}))\).

Howard-Rubin number: 1 AB

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

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