Examples of 'uniformly continuous' in a sentence
Meaning of "uniformly continuous"
In mathematics, this phrase describes a function that maintains a consistent rate of change over its entire domain. A function is uniformly continuous if, for any small change in the input, there is also a small change in the output. This property ensures that the function's behavior remains smooth and predictable
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- That for every real ε > 0 there exists a real δ > 0 such that for all pairs of points x and y in X for which D_X(x,y)<δ, it must be the case that D_Y(f(x),f(y))<ϵ (where D_X and D_Y are the metrics of X and Y, respectively).
How to use "uniformly continuous" in a sentence
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uniformly continuous
Any absolutely continuous function is uniformly continuous.
Uniformly continuous maps will then be proximally continuous.
We say that such a function is uniformly continuous.
The generator of a uniformly continuous semigroup is a bounded operator.
Prove that a function is not uniformly continuous.
Uniformly continuous function.
Any continuous function is almost uniformly continuous.
Also uniformly continuous.
Each almost periodic function is uniformly continuous.
All uniformly continuous functions are continuous with respect to the induced topologies.
Every continuous function is uniformly continuous.
F is uniformly continuous.
We would like to show first that is uniformly continuous.
F is uniformly continuous on ℝ.
Such a function is uniformly continuous.
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In particular, every function which is differentiable and has bounded derivative is uniformly continuous.
We say that f is uniformly continuous if.
Any continuous function on a closed and bounded interval is uniformly continuous.
The product of two uniformly continuous functions might not be uniformly continuous.
Any Hölder continuous function is uniformly continuous.
Then f is uniformly continuous on K.
Because g is continuous on a compact domain, it is uniformly continuous.
The metric maps are both uniformly continuous and Lipschitz, with Lipschitz constant at most one.
On a compact set, it is easily shown that all continuous functions are uniformly continuous.
Every absolutely continuous function is uniformly continuous and, therefore, continuous.
The Heine - Cantor theorem asserts that every continuous function on a compact set is uniformly continuous.
This procedure ultimately gives rise to a uniformly continuous coating film surface.
Because is uniformly continuous ( according to Heine theorem ), there exists such that for all, implies.
The image of a totally bounded subset under a uniformly continuous function is totally bounded.
For instance, any isometry ( distance-preserving map ) between metric spaces is uniformly continuous.
On the other hand, the Cantor function is uniformly continuous but not absolutely continuous.
Since the function p is continuous on compact J, it is uniformly continuous.
Is f uniformly continuous on R?
If X is a finite-dimensional Banach space, then any strongly continuous semigroup is a uniformly continuous semigroup.
Therefore $ f $ is uniformly continuous.
For any α > 0, the condition implies the function is uniformly continuous.
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