Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 279
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 279

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
1:

\(C(\infty,\infty)\):  The Axiom of Choice: Every  set  of  non-empty sets has a choice function.

279:

The Closed Graph Theorem for operations between Fréchet Spaces: Suppose \(X\) and \(Y\) are Fréchet spaces, \(T:X\to Y\) is linear and \(G=\{(x,Tx): x \in X \}\) is closed in \(X\times Y\). Then \(T\) is continuous. Rudin [1991] p. 51.

Comment:

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