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 …

Nov 16, 2023 · I then finish off my proof by stating two theorems, namely that any constant times a continuous function is still continuous and the sum of continuous functions are continuous.

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 …

Sep 18, 2024 · That the preimage of every basis element is open is sufficient for the inverse function to be continuous is seen on page 103 of Munkres' second ed. of Topology. I hope this makes your life …

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 uniformly …

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

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 …