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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 of if and if the order interval is a total subset of ; that is, if the linear span of is a dense subset of [1]

Properties

If 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 dense in [1]

Examples

If then a point in 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 almost everywhere (with respect to ).[1]

A point in is quasi-interior to the positive cone if and only if it is interior to [1]

See also

References

  1. ^ a b c d Schaefer & Wolff 1999, pp. 234–242.

Bibliography