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A remarkable simple closed curve: revisited

Author: O. G. Harrold
Journal: Proc. Amer. Math. Soc. 81 (1981), 133-136
MSC: Primary 57M30; Secondary 57N45
MathSciNet review: 589155
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Abstract: It is shown that the pathology of R. H. Fox's remarkable simple closed curve is in a sense explained below more complicated than that of some examples of the well-known Fox-Artin paper.

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

  • [1] R. H. Bing, Locally tame sets are tame, Ann. of Math. 59 (1954), 145-158. MR 0061377 (15:816d)
  • [2] P. H. Doyle and J. G. Hocking, Some results on tame disks and spheres on $ {E^3}$, Proc. Amer. Math. Soc. 11 (1960), 832-836. MR 0126839 (23:A4133)
  • [3] R. H. Fox and E. Artin, Some wild cells and spheres in three-space, Ann. of Math. 49 (1948), 979-990. MR 0027512 (10:317g)
  • [4] R. H. Fox and O. G. Harrold, The wilder arcs. Topology of $ 3$-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961), Prentice-Hall, Engelwood Cliffs, N.J., 1962, pp. 184-185. MR 0140096 (25:3519)
  • [5] R. H. Fox, A remarkable simple closed curve, Ann. of Math. 50 (1949), 264-265. MR 0030745 (11:45b)
  • [6] W. Graeub, Die semilinear Abbildungen, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1950, pp. 205-272. MR 0042709 (13:152a)
  • [7] O. G. Harrold, Locally tame curves and surfaces in three-dimensional manifolds, Bull. Amer. Math. Soc. 63 (1957), 302. MR 0088718 (19:568g)
  • [8] -, An Additive Index Theorem for certain wildly embedded curves and surfaces (Proc. Conf. Geometric Topology), Academic Press, New York, 1979.
  • [9] E. E. Moise, Affine structures in $ 3$-manifold. VIII, Ann. of Math. 59 (1954), 159-170. MR 0061822 (15:889g)

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Article copyright: © Copyright 1981 American Mathematical Society

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