On Jun 18, 2009, at 2:21 PM, David C. Ullrich wrote:
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.
This simply isn't true.
Charles Yeomans
--
http://mail.python.org/mailman/listinfo/python-list
