Sentence examples for a continuous selection of from inspiring English sources

If f: C → C is a continuous selection of Ω, then Fix(f) is nonempty.

Suppose that f is a continuous selection of F and (F x)subset f(x)+mathbb{R}_^{n}).

Then Since is open, is open in From Theorems 2.1 and 2.2, there exists a continuous selection of and such that for every, (3.10).

Thus f: ℝ n → ℝ n is a continuous selection of Ω with no fixed points and f = h on Fix, which contradicts Lemma 3.9.

Following Theorem 3.1, the sequence (mathcal{S}= (f^{n})) is a virtually stable scheme with (operatorname{Fix}(mathcal{S}) = operatorname{Fix}(f)= operatorname{Fix}(F)), where f is a continuous selection of (P_{F}).

That is, (g_{1}) is a continuous selection of (Fcirc s_{1}) satisfying biglVert g_{1}(x -g_{0}(x -g_{Vert leq Hbigl(F circ s_{1}(x), Fcirc s_{0}(x bigrVertmma_{0} for each (x in X).

As a result of a continuous selection for growth in an endless supply of nutrients or space to grow, cell lines exhibit characteristic changes in expression patterns that distinguish them from corresponding clinical samples.

This implies that there exists a continuous selection h of F: Fix(F) → Pc, cp(ℝ n ) without fixed points.

Then, by Lemma 3.11, there is a continuous selection g of I - Ω such that g(x) ≠ 0 for each x ∈ Fix.

(Saint Raymond [39]) Let K be a compact metric space with dim K < n, X a Banach space and Ω: K → Pc, cp(X) a lower semicontinuous map such that 0 ∈ Ω x) and dim Ω x) ≥ n for every x ∈ K. Then there exists a continuous selection f of Ω such that f(x) ≠ 0 for each x ∈ K. Theorem 3.12.

Assume that the conditions (a -(c) and (f) in Theorem 3.1 and the following conditions are satisfied: (d)' T x, μ) is weakly (η, ϕ, C x -pseudo-mapping with respeC x -pseudo-mappingment and B-u.s.C x -pseudo-mappings on X × {μ0}; (e)' there is a continuous selection t of T on X × {μ0}.