Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!bonnie!akgua!sdcsvax!sdcrdcf!hplabs!hao!seismo!harvard!wjh12!foxvax1!brunix!browngr!jfh 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> Lines: 13 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.