Sentence examples for icu property from inspiring English sources

In the context of hypothesis (e), it is clear that increasing requirement on g together with the ICU property implies the g-ICU property, therefore it is more natural to use the g-ICU property as opposed to the ICU property together with increasing requirement on g.

Now g is increasing and ( X, d, ⪯ ) has the ICU property, this implies that ( X, d, ⪯ ) has the g-ICU property.

ICU property ⇒ ICC property.

For an ordered metric space: ICU property ⇒ ICC property.

Otherwise, suppose that ( g X, d, ⪯ ) has the ICU property.

Notice that under the restriction (g=I), the identity mapping on X, the notions of g-ICU property, g-DCL property, and g-MCB property reduce to ICU property, DCL property, and MCB property, respectively.

g-ICU property ⇒ g-ICC property.

Alternately, suppose that ( X, d, ⪯ ) has the g-ICU property.

For an ordered metric space: g-ICU property ⇒ g-ICC property.

Hence, one needs to replace the MCB property by the g-ICU property which ensures that g ( g x n ) ⪯ g ( z ), so that the given proof can work.

In the context of hypothesis (iii), the continuity of f is not necessary as it can alternately be replaced by the condition that ( X, d, ⪯ ) has the g-ICU property.