On Wed, 17 Jun 2009 05:46:22 -0700 (PDT), Mark Dickinson <dicki...@gmail.com> wrote:
>On Jun 17, 1:26 pm, Jaime Fernandez del Rio <jaime.f...@gmail.com> >wrote: >> 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? > >s/James/Jaime. Apologies. > >> P.S. The snowflake curve, on the other hand, is uniformly continuous, right? > >Yes, at least in the sense that it can be parametrized >by a uniformly continuous function from [0, 1] to the >Euclidean plane. I'm not sure that it makes a priori >sense to describe the curve itself (thought of simply >as a subset of the plane) as uniformly continuous. As long as people are throwing around all this math stuff: Officially, by definition a curve _is_ a parametrization. Ie, a curve in the plane _is_ a continuous function from an interval to the plane, and a subset of the plane is not a curve. Officially, anyway. >Mark -- http://mail.python.org/mailman/listinfo/python-list
