In particular every left amenable discrete semigroup is left reversible by Corollary 2.2.
In this case x is called a d q -limit of { x n }. ( X, d q ) is called left (right) K -sequentially complete if every left (right) K -Cauchy sequence in X converges to a point x ∈ X such that d q ( x, x ) = 0.
In this case x is called a d q -limit of { x n }. (c) ( X, d q ) is called left (right) K -sequentially complete if every left (right) K -Cauchy sequence in X converges to a point x ∈ X such that d q ( x, x ) = 0. .
If every left (right) -Cauchy sequence ( u m : m ∈ N ) in X is left (right) -convergent in X (i.e., S ( u m : m ∈ N ) L − J ≠ ∅ ( S ( u m : m ∈ N ) R − J ≠ ∅ )), then ( X, P ) is called a left (right) -sequentially complete quasi-gauge space.
If every left (right) J -Cauchy sequence ( u m : m ∈ N ) in X is left (right) J -convergent in X ( i.e., S ( u m : m ∈ N ) L − J ≠ ∅ ( S ( u m : m ∈ N ) R − J ≠ ∅ ) ), then ( X, P ) is called a left (right) J -sequentially complete quasi-gauge space.
We say that a quasi-metric space ((X,d)) is complete if every left K-Cauchy net is convergent for (tau_{d^{-1}}), and say that it is sequentially complete if every left K-Cauchy sequence is convergent for (tau_{d^{-1}}).
On almost every left hand was a band indicating not only that they belonged to someone but that they belonged, period.
Taking every left turn on offer in mapping the improbable bond between a gay Parisian businessman and an opportunistic immigrant rent boy, it's a genuinely unexpected tale of love in a hopeless place.
