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 …

Mar 4, 2026 · I was trying to formalize some things about string motion in physics so I could answer more general questions about it and then I got to a point as to see the limit written below. I then …

Jul 2, 2017 · I think we can show that the identity $ (X, \tau_X)$ to $ (X,\tau')$ is sequentially continuous, and it is certainly not continuous. So in a way, being a sequential space is the natural notion here to …

Jul 22, 2010 · The cardinality is at most that of the continuum because the set of real continuous functions injects into the sequence space $\mathbb R^N$ by mapping each continuous function to its …

Then the theorem that says that any continuous function on a compact set is uniformly continuous can be applied. The arguments above are a workaround this.

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 …

The space of bounded continuous functions is not separable Ask Question Asked 13 years, 4 months ago Modified 3 months ago

In view of the correspondence of nondecreasing functions with positive measures, singular continuous functions correspond to singular continuous measures, i.e. an atomless positive Borel measures …

Jan 30, 2024 · Can a discontinuous function have a continuous derivative? Ask Question Asked 2 years, 2 months ago Modified 2 years, 2 months ago

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 …