Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83 based; site hou2g.UUCP Path: utzoo!watmath!clyde!burl!hou3c!hocda!houxm!hou2g!stekas From: stekas@hou2g.UUCP (J.STEKAS) Newsgroups: net.ai Subject: Plane = Sphere ? Message-ID: <194@hou2g.UUCP> Date: Fri, 9-Mar-84 09:25:57 EST Article-I.D.: hou2g.194 Posted: Fri Mar 9 09:25:57 1984 Date-Received: Sat, 10-Mar-84 11:20:13 EST References: <17301@sri-arpa.UUCP> Organization: AT&T Bell Labs, Holmdel NJ Lines: 13 > In fact, the >plane and the sphere are topologically equivalent (the plane is a sphere >if infinite radius) ... This statement has been made so frequently that I think it's time someone took exception. A plane and sphere are NOT topologically equivalent, a sphere has an additional point. That's why plane like coordinate systems mapped to a sphere always have a point where the coordinates are undefined. In any case, spherical and planar maps can both be colored with the same number of colors. Jim