Sentence examples for consequence of the continuity from inspiring English sources

Likewise, a↦a −1 and a↦a 1/2 are continuous over (mathbb {S}^{>0}_{n}), the former being a consequence of the continuity of the determinant operator.

It is an easy consequence of the continuity of d.

Also, if x k (λ0) ≠ 0, then the statement is a consequence of the continuity of x k in λ.

The right-hand side of (3.24) tends to as as a consequence of the continuity of in the uniform operator topology for by the compactness of.

The second term on the right-hand side of (3.20) tends to 0 as as a consequence of the continuity of in the uniform operator topology for.

It is an easy consequence of the continuity of d.   (II) The P d -property is identical with the P-property.

Use of cross-border healthcare may have consequences for the continuity of care, including conflicts in the medical treatment, for the patient.

In consequence, from the continuity of the operator (mathscr{Q}), it follows that (mathscr{Q}v^=v^), (mathscr{Q}u^=u^).

As a consequence, the continuity of the burrow systems made by both species was altered following imidacloprid treatment.

end{aligned} As a consequence, we get the continuity of the single-valued opertor (T_{V}): biglVert T_{V}(x_{1} -T_{V}(x_{2}) bigrVert le frac{1} -T_{V}a}cdotbiglVert V bigl(u^(x_{2}),x_{1} bigrVert bigleu^(x_{2}),x_{2} bigr)bigrVert to0 quadmbox{as } x_{1}to x_{2}.

Aristotle sometimes recognizes infinite divisibility the property of being divisible into parts which can themselves be further divided, the process never terminating in an indivisible as a consequence of continuity as he characterizes the notion.