Re: Peano's space-filling curve
From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 06/07/04
- Next message: Keith A. Lewis: "Re: compositing / decomposing numbers"
- Previous message: Lothar Brendel: "Re: .999... ?= 1"
- In reply to: John Morgan: "Re: Peano's space-filling curve"
- Next in thread: Shmuel (Seymour J.) Metz: "Re: Peano's space-filling curve"
- Messages sorted by: [ date ] [ thread ]
Date: Mon, 07 Jun 2004 18:53:04 +0100
John Morgan wrote:
>
> Here I read that f is continuous and onto. Elsewhere a
> poster tells me that f cannot be all three of '1 to
> 1',continuous and onto. So f is not '1 to 1'? Re-arrange the
> following words to make a well-known phrase, or saying.
> "together., Get, act, your,"
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_
- Next message: Keith A. Lewis: "Re: compositing / decomposing numbers"
- Previous message: Lothar Brendel: "Re: .999... ?= 1"
- In reply to: John Morgan: "Re: Peano's space-filling curve"
- Next in thread: Shmuel (Seymour J.) Metz: "Re: Peano's space-filling curve"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
