Continuous vs Discrete Variables - Mathematics Stack Exchange
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 …
Proving a limit of a measure is continuous
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 …
elementary set theory - Cardinality of set of real continuous functions ...
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 …
What is the intuition for semi-continuous functions?
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
The space of bounded continuous functions is not separable Ask Question Asked 13 years, 4 months ago Modified 3 months ago
Topological properties preserved by continuous maps
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 …
general topology - The product of continuous function is continuous ...
Jun 14, 2020 · The product of continuous function is continuous. Ask Question Asked 5 years, 10 months ago Modified 1 year, 11 months ago
Can a discontinuous function have a continuous derivative?
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
Why not include as a requirement that all functions must be …
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 …
Is a bounded and continuous function uniformly continuous?
Apr 25, 2017 · This function is continuous on $ [-1,1]$, so it is uniformly continuous there. A fortiori on $ (-1,1)$.