Measuring Fractal Dimension ?

[David C. Ullrich]

On Wed, 17 Jun 2009 07:37:32 -0400, Charles Yeomans
<charles at declareSub.com> wrote:

>
>On Jun 17, 2009, at 2:04 AM, Paul Rubin wrote:
>
>> Jaime Fernandez del Rio <jaime.frio at 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.
>
>Isn't (-?, ?) closed?

What is your version of the definition of "closed"?

>Charles Yeomans