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 …

Oct 26, 2010 · An interesting fact is that most (i.e. a co-meager set of) continuous functions are nowhere differentiable. The proof is a consequence of the Baire Category theorem and can be found (as an …

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 …

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 …

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 …

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 …

Jun 23, 2019 · Prove that a function is not uniformly continuous Ask Question Asked 6 years, 8 months ago Modified 6 years, 8 months ago

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

Nov 10, 2021 · Also let $C_b = C_b (X,\mathbb R)$ be the set of continuous bounded functions from $X$ to $\mathbb R$. Under what hypothesis on $X$ and $\mathbb P$ the set $C_b$ is dense in …

Apr 30, 2014 · Show that every continuous periodic function is bounded and uniformly continuous. For boundedness, I first tried to show that since the a periodic function is continuous, it is continuous for …