Dec 14, 2025 · Both discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. I am quite aware that discrete variables are those …

Apr 14, 2015 · Which is continuous and one-to-one on $\mathbb R$, but is not differentiable at $0$. This is of course just one example, but in general, any time you "stick" two functions together at a point …

Mar 6, 2021 · If it's continuously differentiable then it's continuous. All continuous functions are absolutely continuous on a compact set.

Jun 24, 2016 · So one may note that the only functions whose uniform continuity is really interesting to investigate, are the ones defined on an unbounded interval, being globally continuous, non-periodic …

The authors prove the proposition that every proper convex function defined on a finite-dimensional separated topological linear space is continuous on the interior of its effective domain. You can likely …

Sep 18, 2020 · By differentiability theorem if partial derivatives exist and are continuous in a neighborhood of the point then (i.e. sufficient condition) the function is differentiable at that point.

Sep 9, 2024 · The post Is the set of non-differentiable points for a singular continuous function nowhere dense? also seems highly relevant, but I can't parse the answer enough to figure out whether it …

Dec 18, 2025 · I was recently going through General Topology by N. Bourbaki, and found the following definition of topological groups acting continuously on topological spaces (slightly rephrased) : A …

Jun 27, 2025 · Extending the continuous functional calculus to Borel functional calculus Ask Question Asked 8 months ago Modified 8 months ago

Jan 8, 2017 · The reason one refers to this as "continuous spectrum" Historically had nothing to do with continuity; such spectrum was found to fill a continuum, rather than being discrete.