Implications

We have the following indirect implication of form equivalence classes:

372 \(\Rightarrow\) 372
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
372 \(\Rightarrow\) 372

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

Howard-Rubin Number Statement
372:

Generalized Hahn-Banach Theorem:  Assume that \(X\) is a real vector space, \((Z,\preccurlyeq)\) is a Dedekind complete ordered vector space and \(X_0\) is a subspace of \(X\).  If \(\lambda_0 : X_0 \to Z\) is linear and \(p: X\to Z\) is sublinear and if \(\lambda_0 \preccurlyeq p\) on \(X_0\) then \(\lambda_0\) can be extended to a linear map \(\lambda : X\to Z\) such that \(\lambda \preccurlyeq p\) on \(X\). \ac{Schechter} \cite{1996b}

372:

Generalized Hahn-Banach Theorem:  Assume that \(X\) is a real vector space, \((Z,\preccurlyeq)\) is a Dedekind complete ordered vector space and \(X_0\) is a subspace of \(X\).  If \(\lambda_0 : X_0 \to Z\) is linear and \(p: X\to Z\) is sublinear and if \(\lambda_0 \preccurlyeq p\) on \(X_0\) then \(\lambda_0\) can be extended to a linear map \(\lambda : X\to Z\) such that \(\lambda \preccurlyeq p\) on \(X\). \ac{Schechter} \cite{1996b}

Comment:

Back