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From: james@umcp-cs.UUCP
Newsgroups: net.math
Subject: fundamental group
Message-ID: <3536@umcp-cs.UUCP>
Date: Wed, 2-Nov-83 17:59:06 EST
Article-I.D.: umcp-cs.3536
Posted: Wed Nov  2 17:59:06 1983
Date-Received: Sun, 6-Nov-83 07:53:44 EST
Organization: Univ. of Maryland, Computer Science Dept.
Lines: 17

Try this:

	What topological space has the fundamental group {e , 1} ?
By {e , 1}, I mean the (only) two-element group, otherwise known as
the integers mod 2, under addition.

Fundamental Group:

	The fundamental group of a pathwise-connected topological space
is the group of equivalence classes of loops in the space.  A loop is
a continuous map of the interval [0,1] into the space (where 0 and 1 are
mapped to the same point, to close the loop).  Two loops are equivalent
iff they can be continuously deformed into each other (they are homotopic.)
The group operation is by composition of loops (i.e. you map [0,.5] onto
the first loop, and [.5,1] onto the second loop.

  --Jim O'Toole