Sentence examples for complete gauge from inspiring English sources

Then is an ordered and complete gauge space.

Also, ((X,mathcal{T}(mathcal{F}))) is a complete gauge space.

Theorem 3.2 Let ( X, ℱ, ≼ ) be an ordered complete gauge space satisfying the assumption (H).

Let X be a complete gauge structure ({d_{n}mid n inmathbb{N} }) satisfying condition (1).

Let be an ordered complete gauge space and be an operator.

Let X be endowed with a complete gauge structure ({d_{n}mid n in mathbb{N} }) satisfying condition (1).

The completed gauge should make clear to the viewer how the focus area has changed over the three years.

If ( X, P ) is a left (right) -sequentially complete quasi-gauge space and is symmetric, i.e., ∀ α ∈ A ∀ u, v ∈ X { J α ( u, v ) = J α ( v, u ) }, then ( X, T ) is left (right) partially -admissible on X.

If ( X, P ) is a left (right) -sequentially complete quasi-gauge space, then a set-valued dynamic system ( X, T ), T : X → 2 X, is left (right) -admissible on X.

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.

(b) If ( X, P ) is a left (right) -sequentially complete quasi-gauge space and is symmetric, i.e., ∀ α ∈ A ∀ u, v ∈ X { J α ( u, v ) = J α ( v, u ) }, then ( X, T ) is left (right) partially -admissible on X.   (c) It is evident that each left (right) partially -admissible on X a set-valued dynamic system ( X, T ) is left (right) -admissible on X but the converse not necessarily holds.  .