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Pseudocontraction and homotopy of the $ \sin(1/x)$ curve

Author: Hidefumi Katsuura
Journal: Proc. Amer. Math. Soc. 115 (1992), 1129-1138
MSC: Primary 55P99; Secondary 54F99
MathSciNet review: 1092923
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Abstract: We will prove that the space $ \sin 1/x$ curve is not pseudocontractible using itself as the parameter space and that it has finitely many different homotopy equivalent classes of maps.

References [Enhancements On Off] (What's this?)

  • [1] Wayne Lewis, Homogeneous continua and continuous decompositions, Proceedings of the 1983 topology conference (Houston, Tex., 1983), 1983, pp. 71–84. MR 738471
  • [2] Houston Problem Book, Department of Mathematics, University of Houston.

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Keywords: Homotopy, contraction, pseudocontraction, uniform continuity
Article copyright: © Copyright 1992 American Mathematical Society

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