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" …

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 …

May 10, 2019 · In an alternative history, c.d.f.'s might have been defined as FX(a) =P({ω ∈ Ω: X(ω) <a}) F X (a) = P ({ω ∈ Ω: X (ω) <a}) with strict inequality, and then these functions would …

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 …

Nov 14, 2012 · Closure of continuous image of closure Ask Question Asked 12 years, 8 months ago Modified 12 years, 8 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 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 …

A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...