Sentence examples for be a solid vector from inspiring English sources

Theorem 7.2 Let ( Y, ⪯, ≺, → ) be a solid vector space.

Definition 6.2 Let ( Y, ⪯, ≺, → ) be a solid vector space.

Example 9.2 Let ( Y, ⪯, ≺, → ) be a solid vector space, and let X be its positive cone.

Example 9.1 Let X be a nonempty set and let ( Y, ⪯, ≺, → ) be a solid vector space.

Definition 6.1 Let ( Y, ⪯, ≺, → ) be a solid vector space, and let a, b ∈ Y be two vectors with a ≺ b.

An ordered vector space with convergence endowed with a strict vector ordering is said to be a solid vector space.

Y is a solid vector space.

Then Y is a solid vector space called a solid topological vector space.

Then the following statements are equivalent: (i) Y is a solid vector space.

Theorem 6.3 If ( Y, ⪯, ≺, → ) is a solid vector space, then the convergence on Y has the following properties.

Every ordered vector space with convergence can be equipped with a strict vector ordering if and only if it is a solid vector space.