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Tame surfaces and tame subsets of spheres in $ E\sp{3}$


Author: L. D. Loveland
Journal: Trans. Amer. Math. Soc. 123 (1966), 355-368
MSC: Primary 54.78
DOI: https://doi.org/10.1090/S0002-9947-1966-0199850-3
MathSciNet review: 0199850
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  • [1] R. H. Bing, Locally tame sets are tame, Ann. of Math. 59 (1954), 145-158. MR 0061377 (15:816d)
  • [2] -, Approximating surfaces with polyhedral ones, Ann. of Math. 65 (1957), 456-483. MR 0087090 (19:300f)
  • [3] -, An alternative proof that $ 3$-manifolds can be triangulated, Ann. of Math. 69 (1959), 37-65. MR 0100841 (20:7269)
  • [4] -, Conditions under which a surface in $ {E^3}$ is tame, Fund. Math. 47 (1959), 105-139. MR 0107229 (21:5954)
  • [5] -, A surface is tame if its complement is $ 1$-ULC, Trans. Amer. Math. Soc. 101 (1961), 294-305. MR 0131265 (24:A1117)
  • [6] -, Each disk in $ {E^3}$ contains a tame arc, Amer. J. Math. 84 (1962), 583-590. MR 0146811 (26:4331)
  • [7] -, Each disk in $ {E^3}$ is pierced by a tame arc, Amer. J. Math. 84 (1962), 591-599. MR 0146812 (26:4332)
  • [8] -, Approximating surfaces from the side, Ann. of Math. 77 (1963), 145-192. MR 0150744 (27:731)
  • [9] -, Pushing a $ 2$-sphere into its complement, Mich. Math. J. 11 (1964), 33-45. MR 0160194 (28:3408)
  • [10] Morton Brown, Locally flat imbeddings of topological manifolds, Ann. of Math. 75 (1962), 331-341. MR 0133812 (24:A3637)
  • [11] C. E. Burgess, Characterizations of tame surfaces in $ {E^3}$, Trans. Amer. Math. Soc. 114 (1965), 80-97. MR 0176456 (31:728)
  • [12] P. H. Doyle and J. G. Hocking, Some results on tame disks and spheres in $ {E^3}$, Proc. Amer. Math. Soc. 11 (1960), 832-836. MR 0126839 (23:A4133)
  • [13] D. S. Gillman, Side approximation, missing an arc, Amer. J. Math. 85 (1963), 459-476. MR 0160193 (28:3407)
  • [14] O. G. Harrold, Jr., Locally peripherally unknotted surfaces in $ {E^3}$, Ann. of Math. 69 (1959), 276-290. MR 0105660 (21:4399a)
  • [15] O. G. Harrold, Jr., H. C. Griffith, and E. E. Posey, A characterization of tame curves in $ 3$-space, Trans. Amer. Math. Soc. 79 (1955), 12-35. MR 0091457 (19:972c)
  • [16] Witold Hurewicz and Henry Wallman, Dimension theory, Princeton Univ. Press, Princeton, N. J., 1948. MR 0006493 (3:312b)
  • [17] L. D. Loveland, Tame subsets of spheres in $ {E^3}$, Pacific J. Math. (to appear). MR 0225309 (37:903)
  • [18] E. E. Moise, Affine structures in $ 3$-manifolds. VIII, Invariance of knot-types; local tame imbbeddings, Ann. of Math. 59 (1954), 159-170. MR 0061822 (15:889g)
  • [19] R. L. Moore and J. R. Kline, On the most general plane closed set through which it is possible to pass a simple continuous arc, Ann. of Math. 20 (1919), 218-223. MR 1502556
  • [20] G. T. Whyburn, Topological characterization of the Sierpinski curve, Fund. Math. 45 (1958), 320-324. MR 0099638 (20:6077)

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DOI: https://doi.org/10.1090/S0002-9947-1966-0199850-3
Article copyright: © Copyright 1966 American Mathematical Society

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