Ordered topological vector space

In mathematics, specifically in functional analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order ≤ making it into an ordered vector space whose positive cone ${\displaystyle C:=\left\{x\in X:x\geq 0\right\}}$ is a closed subset of X.^[1] Ordered TVSes have important applications in spectral theory.