Continuous Functions

Abstract

If A is a subset of a vector space V over a field 𝕂 (usually 𝕂 = ℝ or 𝕂 = ℂ) the linear span of A is the set $\left\{ {\sum\nolimits_{k = 1}^n {{\alpha _k}{a_k}:{\alpha _k} \in } ,{a_k} \in A,n \in } \right\}$ and the convex hull of A is the set $\left\{ {\sum\nolimits_{k = 1}^n {{\alpha _k}{a_k}:{\alpha _k} \in } ,0 \mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle=}\vphantom{_x}}$}} {\alpha _k},\sum\nolimits_{k = 1}^n {{\alpha _k} = 1,{a_k} \in } A,n \in } \right\}$.