Category:Mazur's Theorem

This category contains pages concerning Mazur's Theorem:

Let $\GF \in \set {\R, \C}$.

Let $\struct {X, \norm {\, \cdot \,} } $ be a normed vector space over $\GF$ with weak topology $w$.

Let $C \subseteq X$ be a convex subset of $X$.

Then:

$\map {\cl_w} C = \map \cl C$

where $\cl_w$ denotes the weak closure.