Sentence examples for partial ordered from inspiring English sources

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

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

Obviously, (X, d, ≤) is a complete partial ordered metric space.

Also, we can find some results on partial ordered fuzzy metric spaces and partial ordered uniform spaces in [16 18], respectively.

((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.

Consider We will use the following partial ordering.

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

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

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).