Sentence examples for be an ordered topological from inspiring English sources

Let be an ordered topological vector space with a closed, pointed, and convex cone with.

Let be an ordered topological space, and an order interval in.

Let be an ordered topological space, a nonempty subset of with ; let have sup-closed values and satisfy hypothesis (H1).

Let be a Hausdorff topological linear space, a nonempty, closed, and convex subset, and be an ordered topological vector space with for all.

Let ((Z,P)) be an ordered topological vector space, E be a nonempty convex subset of a vector space X, and (f: Erightarrow Z) be a vector-valued mapping.

Let be an ordered topological space, is said to be a quasi-separable set in if for any totally ordered set in, there exists a countable set such that is dense in (i.e., for any, there exists such that ).

Assume that is an ordered topological space.

The pair is an ordered topological vector space.

Each cone P induces a partial order ≼ on E by x ≼ y ⇔ y - × ∈ P. x π y will stand for (x ≼ y and x ≠ y), while x ≪ y will stand for y - × ∈ int P. The pair (E, P) is an ordered topological vector space.

In this case E is called an ordered topological vector space.

is called an ordered topological space if for any two sequences and in, and, imply.