Quasi-interior point

Properties

• If X is a separable metrizable locally convex ordered topological vector space whose positive cone C is a complete and total subset of X, then the set of quasi-interior points of C is dense in C.

  Examples

• If then a point in is quasi-interior to the positive cone C if and only it is a weak order unit, which happens if and only if the element contains a function that is > 0 almost everywhere.
• A point in is quasi-interior to the positive cone C if and only if it is interior to C.