What's the difference between continuous and piecewise …
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 …
is bounded linear operator necessarily continuous?
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 …
probability theory - Why does a C.D.F need to be right-continuous ...
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 …
What is a continuous extension? - Mathematics Stack Exchange
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" …
Why are norms continuous? - Mathematics Stack Exchange
Describe why norms are continuous function by mathematical symbols.
Where is $x^x$ continuous? - Mathematics Stack Exchange
May 29, 2016 · In any such branch, the complex logarithm is analytic and therefore continuous on the negative real half-line. To conclude, the answer to your question is that x x is always …
Why is the determinant continuous? - Mathematics Stack Exchange
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 …
Strongly continuous Operator. - Mathematics Stack Exchange
Oct 26, 2015 · I can not understand the notion "strongly continuous operator on a Banach space". Is it the continuity with respect to norm on a Banach space? Can someone kindly explain this …
real analysis - Showing that $\arctan$ is continuous - Mathematics ...
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 …
Difference between continuity and uniform continuity
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 …