Editing Geometry of numbers (section)

==Influence on functional analysis==
{{Main article|normed vector space}}
{{See also|Banach space|F-space}}
Minkowski's geometry of numbers had a profound influence on [[functional analysis]]. Minkowski proved that symmetric convex bodies induce [[normed space|norms]] in finite-dimensional vector spaces. Minkowski's theorem was generalized to [[topological vector space]]s by [[Kolmogorov]], whose theorem states that the symmetric convex sets that are closed and bounded generate the topology of a [[Banach space]].<ref>For Kolmogorov's normability theorem, see Walter Rudin's ''Functional Analysis''. For more results, see Schneider, and Thompson and see Kalton et al.</ref>

Researchers continue to study generalizations to [[star-shaped set]]s and other [[convex set|non-convex set]]s.<ref>Kalton et al. Gardner</ref>