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.

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

You'll find topological properties with indication of whether they are preserved by (various kinds of) continuous maps or not (such as open maps, closed maps, quotient maps, perfect maps, etc.). For …

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 …