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From: jfh@browngr.UUCP (John "Spike" Hughes)
Newsgroups: net.math
Subject: Re: Re: Strange Shapes
Message-ID: <1635@browngr.UUCP>
Date: Wed, 28-Nov-84 09:59:59 EST
Article-I.D.: browngr.1635
Posted: Wed Nov 28 09:59:59 1984
Date-Received: Tue, 4-Dec-84 08:24:41 EST
References: talcott.136, <176@ihnet.UUCP>, <177@ihnet.UUCP> <7116@watrose.UUCP>
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   I think that the proposal "Find a two-dimensional surface with finite
surface area which separates 3-space into two regions, each of which has
infinite volume" has some merit.
  Shall we assume that "2-dimensional surface" means a smooth or polygonal
2-dimensional manifold (i.e. a set that is locally homeomorhic to the plane)?
Or is 'dimension' to be measured in some more abstract way?
  I propose that, initially at least, we restrict to sets which are 'parametric'
surfaces, i.e. are the images of nice functions from 2-space to 3-space. (e.g.
the sphere is the image of (x, y) -----> (cos x cos y, cos x sin y, sin x),
where x goes from -pi/2 to pi/2, and y goes from 0 to 2 pi).

   I suspect that in this case, the answer is that there is no such surface.