Form equivalence class Howard-Rubin Number: 94
Statement: The Classical Ascoli Theorem. For any set \(F\) ofcontinuous functions from \(\Bbb R\) to \(\Bbb R\), the followingconditions are equivalent:\itemitem{(1)} Each sequence in \(F\) has a subsequence thatconverges continuously to some continuous function (notnecessarily in \(F\)).\itemitem{(2)} (a) For each \(x\in {\Bbb R}\), the set \(F(x) = \{f(x) : f\in F\}\) is bounded, and\itemitem{} (b) \(F\) is equicontinuous.\parRhineghost [2000] and Note 10 \item{}{\bf[94 R]} Weak Determinateness. If \(A\) is a subset of\({\Bbb N}^{\Bbb N}\) with the property that\newline\centerline{\((\forall a\in A)(\forall x\in {\Bbb N}^{\Bbb N})\left( x_n = a_n\hbox{ for } n=0 \hbox{ and } n \hbox{ odd } \tox\in A\right)\)}\newlineThen in the game \(G(A)\) one of the two players has a winningstrategy. Rhineghost [2000] and Note 153.
Howard-Rubin number: 94 Q
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