Category:Completion Theorem (Normed Vector Space)
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This category contains pages concerning Completion Theorem (Normed Vector Space):
Let $\GF \in \set {\R, \C}$.
Let $\struct {X, \norm {\, \cdot \,} }$ be a normed vector space.
Then there exists a Banach space $\struct {\widetilde X, \widetilde {\norm {\, \cdot \,} } }$ and a linear isometry $\phi : X \to \widetilde X$ such that $\phi \sqbrk X$ is dense in $\widetilde X$.
Further, the Banach space $\struct {\widetilde X, \widetilde {\norm {\, \cdot \,} } }$ is unique up to isometric isomorphism.
Pages in category "Completion Theorem (Normed Vector Space)"
This category contains only the following page.