Abstract
Most topology texts prove the noncontractibility of the circle as an easy corollary of the computation of its fundamental group or its homology groups. Thus, this property of the circle has become part of a relatively advanced subject: algebraic topology. The noncontractibility of the circle can be proved quite easily using only material from a traditional undergraduate point-set topology course. Furthermore, a large number of interesting and significant consequences of this fact can be obtained without additional mathematical prerequisites. Therefore, a fascinating area of elementary topology has been inaccessible to a substantial number of people who do, in fact, have sufficient background in topology to understand and appreciate it. The purpose of this paper is to try to correct this oversight.
Published Version
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