Example 2.1 Let X = R with a usual ordering.
Example 2.2 Let X = R and ( X, d ) be the usual metric space ordered by a usual ordering ≤.
If X is endowed with a usual ordering ≤, then ( X, ≤, d ) is a totally ordered metric space with ϱ as a P -function of type (A) w.r.t.
When we are experiencing it, loss often feels like an anomaly, a disruption in the usual order of things.
Then one day, as a suspect headed into a coffee shop and prepared to place his usual order, an agent would sidle up and place the order for him.
She said she ate there up to three times a week for several years, having her usual order of a hot dog, fries and a Diet Coke.
The settlements seemed to vindicate Judge Hellerstein's strategy in ordering trials to determine damages before a trial to determine liability, a reversal of the usual order.
— The new kids on the block are not a boy band here, but a threat to the usual order of things at Wimbledon.
Let (X= {1-frac{1}{n}, n=4, 5,ldots } cup{0, 1}cup{2n, n=1, 2, ldots}), where ((X, d, leq)) is a complete partially ordered metric space with a metric d and usual order ≤.
Example 3 Let X = { 0 } ∪ { 1 2 n : n ≥ 1 }, where ( X, d, ≤ ) is a complete partially ordered metric space with a metric d and usual order ≤.
