Sentence examples for be a directed set from inspiring English sources

Now let be a directed set with order and let be a family of locally convex spaces.

A set Λ is said to be a directed set if '≺' is a preorder and every pair of elements of Λ has an upper bound.

A class of sets F ⊂ P is a filter of Λ iff A ∩ B ∈ F for all A, B ∈ F and for every A ∈ F and B ⊃ A we have B ∈ F. An ideal ℐ (resp. a filter ℱ) of Λ is said to be non-trivial iff I ≠ ∅ and Λ ∉ I (resp. F ≠ ∅ and ∅ ∉ F ). Let be a directed set.

(Note that a left reversible semigroup is a directed set).

We can see that (S, ≽) is a directed set.

Then the solution set of problem (1.1) is a directed set.

Let be a totally ordered subset in, where is a directed set.

Since ( N ( X ), ⊃ ) is a directed set, we have ( x + z v ) V ∈ N X X ) is a net in X.

Specifically, (M_{alpha}) is a directed set with varphi M_{alpha}rightarrow { betainGamma beta< alpha } isotone and cofinal.

Since (X, ≼) is a directed set, there exists w ∈ X such that z ≼ w and z' ≼ w.

Analogous arguments show that the set of solutions of (11) in is downwards directed and, therefore, it is a directed set.