Jaime Fernandez del Rio <jaime.f...@gmail.com> writes: > I am pretty sure that a continuous sequence of > curves that converges to a continuous curve, will do so uniformly.
I think a typical example of a curve that's continuous but not uniformly continuous is f(t) = sin(1/t), defined when t > 0 It is continuous at every t>0 but wiggles violently as you get closer to t=0. You wouldn't be able to approximate it by sampling a finite number of points. A sequence like g_n(t) = sin((1+1/n)/ t) for n=1,2,... obviously converges to f, but not uniformly. On a closed interval, any continuous function is uniformly continuous. -- http://mail.python.org/mailman/listinfo/python-list
