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 …

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 …

A function is continuous if the preimage of every open set is an open set. (This is the definition in topology and is the "right" definition in some sense.) The definitions you cite of semicontinuities claim …

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 …

Jun 20, 2018 · We know that differentiable functions must be continuous, so we define the derivative to only be in terms of continuous functions. But then, the fact that differentiable functions are …

Apr 25, 2017 · This function is continuous on $ [-1,1]$, so it is uniformly continuous there. A fortiori on $ (-1,1)$.

Jun 14, 2020 · The product of continuous function is continuous. Ask Question Asked 5 years, 10 months ago Modified 1 year, 11 months ago

Definition of continuous map Ask Question Asked 12 years, 11 months ago Modified 1 year, 8 months ago

May 1, 2015 · A continuous random variable can realise an infinite count of real number values within its support -- as there are an infinitude of points in a line segment. So we have an infinitude of values …