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What is a continuous extension? - Mathematics Stack Exchange
The continuous extension of f(x) at x = c makes the function continuous at that point. Can you elaborate some more? I wasn't able to find very much on "continuous extension" throughout …
probability theory - Why does a C.D.F need to be right-continuous ...
May 10, 2019 · In an alternative history, c.d.f.'s might have been defined as P a P ω Ω X ω a with strict inequality, and then these functions would be continuous from the left rather than from …
Are there any functions that are (always) continuous yet not ...
Are there any examples of functions that are continuous, yet not differentiable? The other way around seems a bit simpler -- a differentiable function is obviously always going to be continuous.
What's the difference between continuous and piecewise …
Oct 15, 2016 · A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a …
is bounded linear operator necessarily continuous?
3 This property is unrelated to the completeness of the domain or range, but instead only to the linear nature of the operator. Yes, a linear operator (between normed spaces) is bounded if …
Proving the inverse of a continuous function is also continuous
Proving the inverse of a continuous function is also continuous Ask Question Asked 11 years, 8 months ago Modified 7 years, 6 months ago
Where is $x^x$ continuous? - Mathematics Stack Exchange
May 29, 2016 · In any such branch, the complex logarithm is analytic and therefore continuous on the negative real half-line. To conclude, the answer to your question is that xx x x is always …
Difference between continuity and uniform continuity
Jan 27, 2014 · To understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function that's continuous on R but not uniformly …
real analysis - Prove that every convex function is continuous ...
The authors prove the proposition that every proper convex function defined on a finite-dimensional separated topological linear space is continuous on the interior of its effective …
Why Do We Care About Hölder Continuity? - Mathematics Stack …
Oct 8, 2021 · Hölder continuous functions do not give rise to useful weak solutions in any context I am aware of: there are notions of weak solutions that are continuous, but the Hölder modulus …
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