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 …

Apr 15, 2026 · 3 Why is the proof that sums, differences, products, and quotients of continuous real-valued functions are continuous placed in the section on metric spaces, even though it seems that it …

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 …

Sep 18, 2023 · But notice that, just as we don't usually consider a pointwise orientation to really be an orientation unless it's continuous, so we also don't usually consider a pointwise frame (that is a map …

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, 2020 · By differentiability theorem if partial derivatives exist and are continuous in a neighborhood of the point then (i.e. sufficient condition) the function is differentiable at that point.

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 …

Mar 7, 2013 · 22 I am self-studying general topology, and I am curious about the definition of the continuous function. I know that the definition derives from calculus, but why do we define it like …

May 13, 2015 · A function is called almost continuous iff the function almost continuous at every point $x \in X$. Question: Is $f$ with countable discontinuities almost continuous?

Sep 9, 2019 · Continuous function and Continuous functor Ask Question Asked 6 years, 7 months ago Modified 6 years, 7 months ago