Editing Hahn–Banach theorem (section)

===Geometric separation===

{{Math theorem
| name = {{visible anchor|Hahn–Banach sandwich theorem}}{{sfn|Narici|Beckenstein|2011|pp=177-220}}
| math_statement = Let <math>p : X \to \R</math> be a sublinear function on a real vector space <math>X,</math> let <math>S \subseteq X</math> be any subset of <math>X,</math> and let <math>f : S \to \R</math> be {{em|any}} map. 
If there exist positive real numbers <math>a</math> and <math>b</math> such that 
<math display=block>0 \geq \inf_{s \in S} [p(s - a x - b y) - f(s) - a f(x) - b f(y)] \qquad \text{ for all } x, y \in S,</math>
then there exists a linear functional <math>F : X \to \R</math> on <math>X</math> such that <math>F \leq p</math> on <math>X</math> and <math>f \leq F \leq p</math> on <math>S.</math>
}}