The continuous extension of f(x) f (x) at x = c 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" …

May 10, 2019 · and, because this is not right-continuous, this is not a valid CDF function for any random variable. Of course, the CDF of the always-zero random variable 0 0 is the right …

Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest …

Mar 1, 2017 · The pasting lemma for finitely many closed sets now says that h h is continuous on X X. (a) would follow from the following lemma: If Y Y is an ordered topological space, L = …

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 R but not uniformly …

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 8, 2017 · @Konstantin : The continuous spectrum requires that you have an inverse that is unbounded. If X X is a complete space, then the inverse cannot be defined on the full space. It …

On the smaller closed interval the derivative is bounded; on the entire open interval the function does have vertical asymptotes and cannot be uniformly continuous. Re Dan Fisher's example …

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 …

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 …