Re: Peano's space-filling curve

From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 06/07/04 

Date: Mon, 07 Jun 2004 18:52:38 +0100

John Morgan wrote:

>
>
> I don't recall I said anything about "this fact" either
> way. Actually, I have only just registered the fact that
> there are bijections both ways due to being "told"
> previously that there was a surjection from [1,0] to
> [1,0]^2. And before you say "yes that's true" I had
> initially assumed that the fact I was being offered a
> surjection implied that there was no bijection. Please, all
> of you, try to get your act together. This might help me
> arrange mine likewise.

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_

Relevant Pages

  • Re: Peanos space-filling curve
    ... John Morgan wrote: ... > poster tells me that f cannot be all three of '1 to ... Any relation to Piers? ... Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html ...
    (sci.math)
  • Re: Peanos space-filling curve
    ... John Morgan wrote: ... so you mentioned bijection. ... Any relation to Piers? ... Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html ...
    (sci.math)
  • Re: Peanos space-filling curve
    ... John Morgan wrote: ... Here are the facts: ... Any relation to Piers? ... Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html ...
    (sci.math)