Editing Hahn–Banach theorem (section)

{{short description|Theorem on extension of bounded linear functionals}}
In [[functional analysis]], the '''Hahn–Banach theorem''' is a central result that allows the extension of [[Bounded operator|bounded linear functionals]] defined on a [[vector subspace]] of some [[vector space]] to the whole space.   The theorem also shows that there are sufficient [[Continuous function (topology)|continuous]] linear functionals defined on every [[normed vector space]] in order to study the [[dual space]]. Another version of the Hahn–Banach theorem is known as the '''Hahn–Banach separation theorem''' or the [[hyperplane separation theorem]], and has numerous uses in [[convex geometry]].