Sentence examples for a complete gauge from inspiring English sources

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

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

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

First, we state the extension of Theorems 3.3 and 3.5 for a cyclic mapping and a complete gauge structure.

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

end{cases} Clearly, ({d_{n}mid n inmathbb{N} }) is a complete gauge structure satisfying condition (1).

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

Theorem 3.3 Let ( X, ℱ, ≼ ) be an ordered complete gauge space and f : X → X be a nondecreasing mapping.

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

Theorem 3.4 Let ( X, ℱ, ≼ ) be an ordered complete gauge space and let f, g : X → X be two continuous mappings such that f is g-nondecreasing, f(X) ⊆ g(X) and the pair {f, g} is compatible.

For all ε > 0, we have ∫ 0 ε a ( t ) d t > 0. Theorem 4.1 Let ( X, ℱ, ≼ ) be an ordered complete gauge space and let f, g : X → X be two continuous mappings such that f is g-nondecreasing, f(X) ⊆ g(X) and the pair {f, g} is compatible.