Sentence examples for a partial ordered from inspiring English sources

Let ( X, ⪯ ) be a partial ordered set.

Definition 1.7 Let ( X, ≤ ) be a partial ordered set.

((C([a,b],K_{C}(mathbb {R})), preceq )) is a partial ordered space.

Let ( X, ⪯ ) be a partial ordered set and F X × X → → X be a mapping.

Let ((K_{C}(mathbb {R}), preceq)) be a partial ordered space, then we have the following properties: (i) ((C([a,b],K_{C}(mathbb {R})), preceq )) is a partial ordered space.

In this section we state some results in a partial ordered metric space with ( γ, ψ, p ) -contractive maps.

A partial ordering $P$ is called ccc if every antichain of $P$ is countable.

For a product X 4 of a partial ordered set ( X, ≤ ), we define a partial ordering in the following way: For all ( x, y, z, w ), ( u, v, r, h ) ∈ X 4, ( x, y, z, w ) ≤ ( u, v, r, h ) ⇒ x ≤ u, y ≥ v, z ≤ r and w ≥ l. (40).

For a product X3 = X × X × X of a partial ordered set (X, ≤), we define a partial ordering in the following way: For all (x, y, z), (u, υ, r) ∈ X3 ( x, y, z ) ≤ ( u, v, r ) ⇔ x ≤ u, y ≥ v and z ≤ r. (2.22).

A set with a partial order ⪯ is called a partially ordered set.

Let ⪰ be a partial order on B satisfying that ( B, ⪰ ) is a partially ordered vector space.