Apr 16, 2023 · Since the Sobolev space only cares about function up to a set of measure zero, we could ask questions about whether functions in the space are continuous, strongly …

Nov 22, 2025 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and …

To find examples and explanations on the internet at the elementary calculus level, try googling the phrase "continuous extension" (or variations of it, such as "extension by continuity") …

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 …

12 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 …

Apr 25, 2017 · This function is continuous on $ [-1,1]$, so it is uniformly continuous there. A fortiori on $ (-1,1)$.

Here you want to refer to the topology of the latter as a normed space, which does not depend on the norm since they are all equivalent in finite dimension. Then the determinant is a polynomial …

Feb 22, 2015 · The projection $ (x,y)\mapsto x$ is a linear transformation and in finite dimensional space $\Bbb R^2$ it's continuous. The same for the second projection and you know the rest …

Aug 1, 2017 · @user8469759 My goal isn't to prove that x^3 is continuous efficiently, but to prove it using epsilon-delta as practice.

Nov 17, 2013 · @user1742188 It follows from Heine-Cantor Theorem, that a continuous function over a compact set (In the case of $\mathbb {R}$, compact sets are closed and bounded) is …