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 …

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 …

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 …

Jul 28, 2017 · I have heard of functions being Lipschitz Continuous several times in my classes yet I have never really seemed to understand exactly what this concept really is. Here is the definition. …

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 …

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

Continuous time models are useful when the dynamics you are interested in are fine enough to be approximated as a continuous process. Moreover, it is a common misconception that somehow …