Editing Linear span (section)

=== A useful lemma ===
Let {{mvar|X}} be a normed space and let {{mvar|E}} be any non-empty subset of {{mvar|X}}. Then
{{ordered list
 |list-style-type=lower-alpha
 | <math>\overline{\operatorname{Sp}}(E)</math> is a closed linear subspace of ''X'' which contains ''E'',
 | <math>\overline{\operatorname{Sp}}(E) = \overline{\operatorname{Sp}(E)}</math>, viz. <math>\overline{\operatorname{Sp}}(E)</math> is the closure of <math>\operatorname{Sp}(E)</math>,
 | <math>E^\perp = (\operatorname{Sp}(E))^\perp = \left(\overline{\operatorname{Sp}(E)}\right)^\perp.</math>
 | <math>(E^\perp)^\perp = ((\operatorname{Sp}(E))^\perp)^\perp = \overline{\operatorname{Sp}(E)}.</math>
}}

(So the usual way to find the closed linear span is to find the linear span first, and then the closure of that linear span.)