The continuous extension of f(x) f (x) at x = c x = c makes the function continuous at that point. Can you elaborate some more? I wasn't able to find very much on "continuous extension" …

Oct 15, 2016 · A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a …

May 10, 2019 · F(x) is right-continuous. So the right-continuous property has a place of prominence in this fundamental question. This fact is useful to resolve this natural question: …

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 R but not uniformly …

Differentiability is a stronger condition than continuity. If f is differentiable at x = a, then f is continuous at x = a as well. But the reverse need not hold. Continuity of f at x = a requires only …

The authors prove the proposition that every proper convex function defined on a finite-dimensional separated topological linear space is continuous on the interior of its effective …

In general, is a bounded linear operator necessarily continuous (I guess the answer is no, but what would be a counter example?) Are things in Banach spaces always continuous?

Aug 4, 2022 · So, there will be a discontinuity at time k. Isn't this violating the definition of continuous stochastic process or is it that I have to keep ω ω constant throught out the …

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, …

6 All metric spaces are Hausdorff. Given a continuous bijection between a compact space and a Hausdorff space the map is a homeomorphism. Proof: We show that f f is a closed map. Let K …