8 июн. 2011 г. · If f is continuous on a closed bounded interval, it is uniformly continuous there. This is a consequence of the Heine-Borel theorem.

13 янв. 2015 г. · The key observation is that the definition of uniform continuity becomes the definition of continuity when you look to a particular point y=a.

18 окт. 2014 г. · I understand the definition of uniform continuity, but wanted some suggestions to prove that a function is or isn't uniformly continuous.

23 окт. 2021 г. · Proof: Assume f:K→R is continuous at every point of a compact set K⊆R. To prove that f is uniformly continuous on K we argue by contradiction.

20 янв. 2014 г. · I try to prove: If g is a continuous function on (a,b) then g is uniformly continuous on (a,b) if and only if it is possible to define values g(a) and g(b) at ...

29 мар. 2015 г. · Uniform continuity of a function is equivalent to a function satisfying a Lipschitz condition. That is ‖f(x)−f(y)‖≤M‖x−y‖. The last bit of the ...

6 дек. 2012 г. · Proof that if f is uniformly continuous then for every Cauchy sequence (xn) with a<xn<b f(xn) is also cauchy.

4 янв. 2015 г. · We say that f is uniformly continuous if, for every ϵ>0, there exists a δ>0 such that f(x) and f(x0) are ϵ-close whenever x,x0∈X are to points ...

17 нояб. 2013 г. · To show uniformly continuity I must show for a given ϵ>0 there exists a δ>0 such that for all x1,x2∈R we have |x1−x2|<δ implies that |f(x1)−f(x2) ...

26 сент. 2021 г. · New concept: A function is uniformly continuous if, when given ε>0,∃ δ>0 such that |x1−x2|<δ⟹|f(x1)−f(x2)|<ε, i.e. for each ε>0, you can find δ> ...