Form Classes

Form equivalence class Howard-Rubin Number: 0

Statement:

The Modified Ascoli Theorem: For any set \(F\) of continuous functions from \(\Bbb R\) to \(\Bbb R\), the following conditions are equivalent:

  1. Each sequence in \(F\) has a subsequence that converges continuously to some continuous function (not necessarily in \(F\)).
    1. For each countable subset \(G\) of \(F\) and each\(x\in {\Bbb R}\), the set \(G(x) = \{ g(x) : g\in G\}\) is bounded, and
    2. Each countable subset of \(F\) is equicontinuous.
    \par\ac{Rhineghost} \cite{2000}

    Howard-Rubin number: 0 AS

    Citations (articles):

    Connections (notes): Note [10] Topology definitions

    References (books):

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