27 янв. 2014 г. · As observed by Siminore, continuity can be expressed at a point and on a set whereas uniform continuity can only be expressed on a set.

5 мая 2018 г. · The main difference is that continuity is a point-wise concept, you need to control the function in a neighborhood of a given point when you ...

24 апр. 2015 г. · Uniform: A curve is uniformly continuous, if it for any given height 2ε is possible to find a width 2δ of a window that works for the entire ...

6 сент. 2014 г. · Continuity is a condition on the function for given single points in the domain, while uniform continuity is a condition on the function for ...

3 мар. 2017 г. · The difference in the definitions comes in the fact that for continuity first you fix y∈A and then you find δ, while for uniform continuity you ...

26 апр. 2012 г. · A continuous function is uniformly continuous if the metric space is compact, and if each continuous function is uniformly continuous, the metric space is ...

17 янв. 2016 г. · In other words, if a function is uniformly continous in X then it is continous in X, but the contrary might not always be true. As an example, ...

12 окт. 2019 г. · Continuity is defined at a point while uniform continuity is defined on a set. If a function f:X→Y is continuous at every ...

12 мая 2014 г. · A function is uniformly continuous if for any pair of points x,y that is close enough, the values f(x) and f(y) will be close as well. For ...

24 мар. 2013 г. · A function is uniformly continuous if, for every (possibly infinite/infinitesimal) x and y, if x−y is infinitesimal, then f(x)−f(y) is infinitesimal.