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 …

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 …

Sep 2, 2024 · Prove $\ln (x)$ is continuous using $\epsilon-\delta$ Ask Question Asked 13 years ago Modified 1 year, 6 months ago

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 …

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 $\mathbb R$ but not uniformly …

Sep 18, 2024 · The graph of a continuous function is a topological manifold Ask Question Asked 1 year, 5 months ago Modified 1 year, 5 months ago

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 …

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 …

Let A be the set of matrix of type \\begin{bmatrix} a&0\\\\ 0 & a^{-1} \\end{bmatrix} where a is a positive number. How to show that if $\\phi$ is a Group homomorphism from A to $\\mathbb...

Prove the absolute value function of a continuous function is continuous [duplicate] Ask Question Asked 12 years, 4 months ago Modified 11 years, 8 months ago