Re: Peano's space-filling curve

From: John Morgan (john.morgan_at_REMOVECAPSataraxie.fr)
Date: 06/10/04 

Date: Thu, 10 Jun 2004 11:40:32 +0200

Michael Stemper <mstemper@siemens-emis.com> wrote in message
news:200406091749.i59Hn1C42456@mickey.empros.com...
> In article <2ie15fFmb6g6U3@uni-berlin.de>, John Morgan
writes:
>
> Thanks for the kind words. One misunderstanding that I
> should correct, however, is that I *am* a layperson. I do
> software project management for a living.

Aha. That explains why you were very sensitive to my
predicament

> Actually, Wikipedia already has an entry:
> <http://en.wikipedia.org/wiki/Cardinality>

I'll have a read and see how well I think they've done

> >> In other words, it is impossible to find a function
> >> f:[0,1]->[0,1]^2 which is one-to-one, onto *and*
> >> continuous.

> >Is this true for all functions? If not, for what class of
> >function(s) has it been proved?

> for any function at all, it's true
> that the function doesn't have *all* of those properties.

I never knew that, or if I did it hadn't registered. Is the
corollary true? If a transformation of I --> I^2 is
discovered that is 1to1, onto and continuous then it cannot
be called a function.

<snip>

The rest I have now got sorted in my mind, I think. Luckily
there's no exam on the way - of my maths knowledge, that is
;-).

Cheers

John

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