Sentence examples for an ordered subset of from inspiring English sources

Let ( C, ⪯ ) be an ordered subset of a quasi-Banach space ( X, ∥ ⋅ ∥, K ).

PA-GFP photoactivation with light polarized parallel or perpendicular to the fiber axis photo-induced an ordered subset of single probes within a differently ordered set of cross-bridges.

We define a valid disjoint fragment chain C as an ordered subset of Fset involving k≤ K fragments, (F1, F2,…, F k ), such that (i) for each pair of subsequent fragments F i, F i +1 (subsequent fragments are said to be chained) we have F i. te< F i +1.

Theorem 3.10 Let ( C, ⪯ ) be a nonempty ordered subset of a quasi-Banach space ( X, ∥ ⋅ ∥, K ), where 1 ≤ K < 2, and let d : X × X → R + be such that d ( x, y ) = ∥ x − y ∥.

A linearly ordered subset of X is called a chain.

In particular, if (F f)) is a totally ordered subset of X, then f has a unique fixed point.

On the other hand, since X is a totally ordered set, hence (F f,g)) is a totally ordered subset of X.

Particularly, if (F f)) is a totally ordered subset of X, then f and g have a unique common fixed point.

In Section 2, we define and study summability and absolute summability of a family ( x α ) α ∈ Λ in a normed space when the index set Λ is a well ordered subset of R ∪.

Let be a totally ordered subset of.

Let be a totally ordered subset of and consider.