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 …

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 …

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 …

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 Ask Question Asked 11 years, 8 months ago Modified 7 years, 6 months ago

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 …

Jan 13, 2012 · the difference is in definitions, so you may want to find an example what the function is continuous in each argument but not jointly

Jul 21, 2020 · Is the derivative of a differentiable function always continuous? My intuition goes like this: If we imagine derivative as function which describes slopes of (special) tangent lines …

Aug 19, 2022 · The MIT supplementary course notes you linked to give — and use — the following (non-standard) definition: We say a function is continuous if its domain is an interval, …

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.