The phrase "a unique element in" is correct and usable in written English.
It can be used when describing something that stands out or is distinct within a particular context or category.
Example: "The artist's use of color is a unique element in her latest collection, setting it apart from her previous works."
Alternatives: "a distinctive feature in" or "a singular aspect of".
Then, for any, there exists a unique element in such that for all.
Then, for any, there exists a unique element in such that (2.4).
A function is locally -invertible at if for any point in there exists a unique element in such that If is locally -invertible at each then we say that is locally -invertible.
Among other things it is shown that every maximal regular left (right, two sided) ideal in A′ is either weak∗ dense or is the annihilator of a unique element in the spectrum of Ap(G).
Then ({mathrm{P}}_{n}(f;x) ) is a unique element in the space of all polynomials of degree at most n, say (mathcal{P}_{n}), which solves the interpolation problem {mathrm{P}}_{n}(f;x_{j})=f(x_{j}),quad j=0,1,2,ldots,n.
For any x in H, there exists a unique element in C, which is denoted by P C x, such that ||x - P C x|| ≤ ||x - y|| for all y in C. We call P C the metric projection of H onto C. It is well-known that P C is a nonexpansive mapping from H onto C, and ⟨ x - P C x, P C x - y ⟩ ≥ 0 for all x ∈ H, y ∈ C ; (1).
A lower spring ordered transversal space is a nonempty partially ordered set X (with ordering ) together with a given lower spring ordered transverse A on X, where every increasing sequence ({u_{n}}_{ninBbb{N}}) of elements in ((a, b]) has a unique element u in ((a, b]) as limit (in notation (u_{n}to u) ((ntoinfty))).
Let C be a nonempty, closed, and convex subset of a strictly convex and reflexive Banach space E. Then we know that, for any (x in E), there exists a unique element (z in C) such that (|x-z| leq|x-y|) for all (y in C).
Then, for any (x in E), there exists a unique element (z in K) such that (|x - z| le|x - y|), (forall y in K).
(1) If E is a reflexive and strictly convex Banach space and C is a nonempty closed and convex subset of E, then for each (x in E) there exists a unique element (v in C) such that (Vert x - v Vert = inf { Vert x - y Vert :y in C}).
If E is a reflexive and strictly convex Banach space and C is a nonempty closed and convex subset of E, then for each (x in E) there exists a unique element (v in C) such that (Vert x - v Vert = inf { Vert x - y Vert :y in C}).
