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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" …
probability theory - Why does a C.D.F need to be right-continuous ...
May 10, 2019 · This function is always right-continuous. That is, for each x ∈ Rk we have lima ↓ xFX(a) = FX(x). My question is: Why is this property important? Is there any capital result in …
What is the difference between "differentiable" and "continuous"
I have always treated them as the same thing. But recently, some people have told me that the two terms are different. So now I am wondering, What is the difference between "differentiable" …
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?
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 …
functional analysis - continuity in the strong topology implies ...
I have to prove that if T: (E, ‖ ⋅ ‖E) → (F, ‖ ⋅ ‖F) is a continuous and linear operator, and xh ⇀ x in E, than Txh ⇀ Tx in F. So we know that T is continuous with respect to the strong topologies, …
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 …
Proving the inverse of a continuous function is also continuous
Proving the inverse of a continuous function is also continuous Ask Question Asked 11 years, 8 months ago Modified 7 years, 6 months ago
real analysis - Proof that $f (x) = x^2$ is continuous ($\delta ...
Aug 1, 2017 · From conclusions drawn at the end of 1 1 and 2 2, we have shown that f(x) f (x) is continuous on x ∈ R x ∈ R I just started learning about ϵ − δ ϵ − δ.
real analysis - Prove that every convex function is continuous ...
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 …
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