Re: Peano's space-filling curve

From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 06/09/04 

Date: Wed, 09 Jun 2004 18:35:01 +0100

John Morgan wrote:

>
> OK. so you mentioned bijection. Can you accept that as far
> back as May 19 I had no clear idea of the significance of
> this mention. Back then everyone was telling me; nobody was
> showing me.
 

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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