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 · and, because this is not right-continuous, this is not a valid CDF function for any random variable. Of course, the CDF of the always-zero random variable 0 0 is the right …

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" …

3 This property is unrelated to the completeness of the domain or range, but instead only to the linear nature of the operator. Yes, a linear operator (between normed spaces) is bounded if …

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 R but not uniformly …

Why is the determinant as a function from Mn(R) M n (R) to R R continuous? Can anyone explain precisely and rigorously? So far, I know the explanation which comes from the facts that …

Jan 5, 2016 · As such, arctan arctan is continuous. If you define arctan arctan by integrals or power series the result is immediate (the first by the Lipshitz continuity of the indefinite integral …

Apr 25, 2017 · This answer is wrong. Although its a nice counterexample to show that a bounded function on a closed, but unbounded interval is not necessarily uniformly continuous.

is continuous but not surjective. The function x ↦x2 x ↦ x 2 from the set of all rational numbers into itself is continuous and not surjective, and does not even take all intermediate values …

What is an example of an open map (0, 1) → R (0, 1) → R which is not continuous? Is it even possible for one to exist? What about in higher dimensions? The simplest example I've been …