Quasi-interior point

In mathematics, specifically in order theory and functional analysis, an element

of an ordered topological vector space

is called a quasi-interior point of the positive cone

and if the order interval

is a total subset of

; that is, if the linear span of

is a dense subset of

is a separable metrizable locally convex ordered topological vector space whose positive cone

is a complete and total subset of

then the set of quasi-interior points of

is quasi-interior to the positive cone

if and only it is a weak order unit, which happens if and only if the element (which recall is an equivalence class of functions) contains a function that is

is quasi-interior to the positive cone