Re: Peano's space-filling curve
From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 06/10/04
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Date: Thu, 10 Jun 2004 19:11:57 +0100
John Morgan wrote:
>
> 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.
Here are the facts:
(i) there is a bijection f : [0,1] -> [0,1]^2,
(ii) there is a continuous surjection g : [0,1] -> [0,1]^2,
(iii) there is no continuous bijection h : [0,1] -> [0,1]^2.
>
> John
Any relation to Piers?
-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html "Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9" Francis Wheen, _How Mumbo-Jumbo Conquered the World_
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