Characterization of taming sets on $2$-spheres
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References
- R. H. Bing, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 465–483. MR 87090
- R. H. Bing, Each disk in $E^{3}$ contains a tame arc, Amer. J. Math. 84 (1962), 583–590. MR 146811, DOI 10.2307/2372864
- R. H. Bing, Each disk in $E^{3}$ is pierced by a tame arc, Amer. J. Math. 84 (1962), 591–599. MR 146812, DOI 10.2307/2372865
- R. H. Bing, Pushing a 2-sphere into its complement, Michigan Math. J. 11 (1964), 33–45. MR 160194
- R. H. Bing, Improving the side approximation theorem, Trans. Amer. Math. Soc. 116 (1965), 511–525. MR 192479, DOI 10.1090/S0002-9947-1965-0192479-1
- C. E. Burgess and J. W. Cannon, Tame subsets of spheres in $E^{3}$, Proc. Amer. Math. Soc. 22 (1969), 395–401. MR 242135, DOI 10.1090/S0002-9939-1969-0242135-5
- C. E. Burgess and L. D. Loveland, Sequentially $1-\textrm {ULC}$ surfaces in $E^{3}$, Proc. Amer. Math. Soc. 19 (1968), 653–659. MR 227962, DOI 10.1090/S0002-9939-1968-0227962-1 J. W. Cannon, Spheres that are tame modulo tame sets, Notices Amer. Math. Soc. 15 (1968), 519. Abstract #656-56.
- 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 126839, DOI 10.1090/S0002-9939-1960-0126839-2 W. T. Eaton, Tameness of certain types of spheres, Notices Amer. Math. Soc. 15 (1968), 510. Abstract #656-28.
- Ralph H. Fox and Emil Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979–990. MR 27512, DOI 10.2307/1969408
- David S. Gillman, Side approximation, missing an arc, Amer. J. Math. 85 (1963), 459–476. MR 160193, DOI 10.2307/2373136 Norman Hosay, Conditions for tameness of a $2$-sphere which is locally tame modulo a tame set, Notices Amer. Math. Soc. 9 (1962), 117. Abstract #589-43. —, The sum of a real cube and a crumpled cube is ${S^3}$, Notices Amer. Math. Soc. 10 (1963), 666. Abstract #607-17. Norman Hosay, Some sufficient conditions for a continuum on a $2$-sphere to lie on a tame $2$-sphere, Notices Amer. Math. Soc. 11 (1964), 370-371. Abstract #612-64.
- Lloyd L. Lininger, Some results on crumpled cubes, Trans. Amer. Math. Soc. 118 (1965), 534–549. MR 178460, DOI 10.1090/S0002-9947-1965-0178460-7
- F. M. Lister, Simplifying intersections of disks in Bing’s side approximation theorem, Pacific J. Math. 22 (1967), 281–295. MR 216484
- L. D. Loveland, Tame subsets of spheres in $E^{3}$, Pacific J. Math. 19 (1966), 489–517. MR 225309
- C. D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1–26. MR 90053, DOI 10.2307/1970113 H. Seifert and W. Threlfall, Lehrbuch der Topologie, Teubner, Leipzig, 1934. Warren White, A $2$-sphere in ${E^3}$ is tame if it is $1$-LC through each complementary domain, Notices Amer. Math. Soc. 15 (1968), 84. Abstract #653-24.
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 147 (1970), 289-299
- MSC: Primary 54.78
- DOI: https://doi.org/10.1090/S0002-9947-1970-0257996-6
- MathSciNet review: 0257996