Measuring Fractal Dimension ?
David C. Ullrich
ullrich at math.okstate.edu
Thu Jun 18 20:21:50 CEST 2009
On Wed, 17 Jun 2009 05:46:22 -0700 (PDT), Mark Dickinson
<dickinsm at gmail.com> wrote:
>On Jun 17, 1:26 pm, Jaime Fernandez del Rio <jaime.f... at gmail.com>
>> On Wed, Jun 17, 2009 at 1:52 PM, Mark Dickinson<dicki... at 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?
>> 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.
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