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 …

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 …

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 …

May 21, 2012 · 72 I found this comment in my lecture notes, and it struck me because up until now I simply assumed that continuous functions map closed sets to closed sets. What are some …

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 …

Jun 6, 2015 · Assume the function is continuous at x0 x 0 Show that, with little algebra, we can change this into an equivalent question about differentiability at x0 x 0. With this little bit of …

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 …

Proving the inverse of a continuous function is also continuous Ask Question Asked 11 years, 8 months ago Modified 7 years, 6 months ago

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 …

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 …