Measuring Fractal Dimension ?

Paul Rubin http
Fri Jun 19 02:40:55 CEST 2009


David C. Ullrich <ullrich at math.okstate.edu> writes:
> >> 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"?

I think the whole line is closed, but I hadn't realized anyone
considered the whole line to be an "interval".  Apparently they do.
So that the proper statement specifies compactness (= closed and
bounded) rather than just "closed".



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