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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