11 окт. 2012 г. · Is there a relationship between uniform continuity and uniform convergence? For example, suppose {fn} is a sequence of functions each of which ...

3 нояб. 2014 г. · Yes, if fn→f uniformly , fn is continuous ∀n, then f is continuous. Here is the idea of proof. In your example, f is continuous and bounded, ...

11 сент. 2017 г. · So the difference is that in PWC the number N depends on x while in UC it does not which means just one N works for all x in [a,b].

26 авг. 2016 г. · We know that uniform convergence of continuous functions implies the continuity of the limit. I'm wondering if the inverse is true.

24 мая 2018 г. · If you know the proof that a sequence of continuous functions which converges uniformly has a continuous limit, then a similar proof should show ...

27 янв. 2019 г. · We know that uniform convergence preserves continuity. We only need to make the case that the individual functions are continuous. We know that ...

17 окт. 2021 г. · I know and understand the definition of uniform continuity and uniform convergence, but it is not clear to me how the latter is an extension ...

14 мая 2020 г. · For every ε/3>0 there is a natural number N≥1 such that for every x∈X we have that dY(f(n)(x),f(x))<ε/3 for every n≥N.

19 мар. 2023 г. · ... continuous functions it explains more conceptually why uniform convergence on bounded intervals preserves continuity. – Anne Bauval.

12 янв. 2018 г. · @user8734617 Global uniform convergence implies uniform continuity of the limit. For the case of the domain being R, I state that explicitly in ...