On Wed, Jun 17, 2009 at 1:52 PM, Mark Dickinson<dicki...@gmail.com> wrote: > Maybe James is thinking of the standard theorem > that says that if a sequence of continuous functions > on an interval converges uniformly then its limit > is continuous?
Jaime was simply plain wrong... The example that always comes to mind when figuring out uniform convergence (or lack of it), is the step function , i.e. f(x)= 0 if x in [0,1), x(x)=1 if x >= 1, being approximated by the sequence f_n(x) = x**n if x in [0,1), f_n(x) = 1 if x>=1, where uniform convergence is broken mostly due to the limiting function not being continuous. I simply was too quick with my extrapolations, and have realized I have a looooot of work to do for my "real and functional analysis" exam coming in three weeks... Jaime P.S. The snowflake curve, on the other hand, is uniformly continuous, right? -- (\__/) ( O.o) ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes de dominación mundial. -- http://mail.python.org/mailman/listinfo/python-list
