Sentence examples for be an ordered metric from inspiring English sources

Let ((X,d,preceq)) be an ordered metric space.

Let ((X,preceq,d)) be an ordered metric space.

Let ( X, d, ⪯ ) be an ordered metric space.

Definition 2.1 Let ( X, d, ⪯ ) be an ordered metric space.

Let (( mathcal{X },d,preceq )) be an ordered metric space.

Let ( X, ⪯, d ) be an ordered metric space and A, B ⊆ X.

From Example 3.5, any arbitrary Riesz space (vector lattice) ( X, ≽ X ) is an ordered metric space with the ordered metric induced by its (ordered) absolute values.

Then ( X, d, ⪯ ) is an ordered metric space.

Example 3.2 The metric defined on a metric space is an ordered metric; and therefore, every metric space is an ordered metric space.

Notice now that if ( X, d, ≤ ) is an ordered metric space, then ( Z, d ˜, ⪯ ) is an ordered generalized metric space.

Then d is an ordered metric; and therefore, every Banach space with the metric induced by its norm is an ordered metric space (where the metric d is defined by d ( u, v ) = ∥ u − v ∥, for every u, v ∈ B ). Example 3.4 Every cone metric on a nonempty set is an ordered metric; and therefore, every cone metric space is an ordered metric space.