Form equivalence class Howard-Rubin Number: 14
Statement: Patching Lemma: Let \(L\) be a local system of \(S\)(that is, \(L\subseteq\Cal P(S)\) and for each finite \(E\subseteq S\),there exists \(H\in L\) such that \(E\subseteq H\)). Let \(F\) be a set and\(n\) a positive integer. Suppose that for each \(H\in L\), there is afunction \(f_{H}: H^{n}\rightarrow F\) and \(\left\{f_{H}(x): H\in L\right\}\)is finite for each \(x\in S^{n}\). Then there is a function \(f:S^{n}\rightarrow F\) such that for any finite subset \(K\subseteq S^{n}\),there is an \(H\in L\) with \(K \subseteq H^{n}\) and \(f\) and \(f_{H}\) agreeon K. Hickin/Plotkin [1976] and Note 83.
Howard-Rubin number: 14 AR
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