What is a continuous extension? - Mathematics Stack Exchange
There are other ways a function can be a continuous extension, but probably the most basic way (and likely about the only way you'll see in elementary calculus) is that you have a function …
What's the difference between continuous and piecewise …
Oct 15, 2016 · A piecewise continuous function doesn't have to be continuous at finitely many points in a finite interval, so long as you can split the function into subintervals such that each …
Where is $x^x$ continuous? - Mathematics Stack Exchange
May 29, 2016 · The idea of continuity of a function is something I come across quite regularly, but I've never really understood it well. I'm trying to fix that by looking at some interesting …
probability theory - Why does a C.D.F need to be right-continuous ...
May 10, 2019 · This fact is useful to resolve this natural question: Let $\{X_i\}_{i=1}^{\infty}$ be i.i.d. random variables uniform over $[-1,1]$.
What is the difference between "differentiable" and "continuous"
$\begingroup$ @user135626: What I wrote is correct. You are misreading it. I'm not saying the derivative is zero, I'm saying that if the derivative exists, the numerator of the difference …
Difference between continuity and uniform continuity
Jan 27, 2014 · I understand the geometric differences between continuity and uniform continuity, but I don't quite see how the differences between those two are apparent from their definitions. …
The definition of continuous function in topology
Mar 7, 2013 · Sometimes it is useful to think of the notion of a 'continuous' function as more 'primitive' than the notion of a 'topology'. For example: Subspace topology is what makes the …
is bounded linear operator necessarily continuous?
Added @Dimitris's answer prompted me to mention, beyond the fact that the implication on normed spaces indeed is an equivalence, that it's the converse which holds in the wider …
Proving the inverse of a continuous function is also continuous
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
real analysis - Prove that every convex function is continuous ...
Is there an alternative proof of the fact that a real-valued convex function defined on an open interval of the reals is continuous? Since in general convex functions are not continuous nor …