The phrase "a continuous extension" is correct and usable in written English.
It can be used in contexts where you are describing something that is ongoing or uninterrupted in its expansion or development.
Example: "The project aims to create a continuous extension of the existing infrastructure to accommodate future growth."
Alternatives: "an ongoing expansion" or "a seamless addition".
Beginning with Princes street, the wide boulevard running along the far shore of the North Loch, the New Town of Edinburgh was intended to be just that: not a continuous extension of the city centre but constructed apart, to an entirely different design, philosophy and layout.
Therefore z has a continuous extension z ∗ on [ t 0, η z ].
This forces (mathbf {C}^_{gamma}f) to admit a continuous extension to (Omegacup gamma).
A natural question to ask is whether (mathbf{C}^_{gamma}f) has a continuous extension to (Omegacupgamma).
By [5, Proposition 2.6] the operator (gamma (z)) is bounded and hence admits a continuous extension onto (mathcal {H}).
where Γ x is the gamma function [20], which is a continuous extension of the factorial (Γ(n + 1) = n !).
To get all continuous extension of (4.2), we consider (4.3).
Three possibilities are considered in this paper: (1) the classical space time Taylor expansion, in which time derivatives are obtained from known space-derivatives by the Cauchy Kovalewsky procedure; (2) a local continuous extension Runge Kutta scheme and (3) a local space time Galerkin predictor with a version suitable for stiff source terms.
Any subsolution for Ψ has a (Lipschitz) continuous extension to the closed unit disk U ¯.
The function f(r) = br has a unique continuous extension from the rational numbers to the real numbers for each b > 0. But when b < 0, the function f is not even continuous on the set of rational numbers r for which it is defined.
In particular, we will consider E 1 which is a parameter-independent continuous extension operator.
