Tame surfaces and tame subsets of spheres in $E^{3}$
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- by L. D. Loveland
- Trans. Amer. Math. Soc. 123 (1966), 355-368
- DOI: https://doi.org/10.1090/S0002-9947-1966-0199850-3
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References
- R. H. Bing, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145–158. MR 61377, DOI 10.2307/1969836
- R. H. Bing, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 465–483. MR 87090
- R. H. Bing, An alternative proof that $3$-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37–65. MR 100841, DOI 10.2307/1970092
- R. H. Bing, Conditions under which a surface in $E^{3}$ is tame, Fund. Math. 47 (1959), 105–139. MR 107229, DOI 10.4064/fm-47-1-105-139
- R. H. Bing, A surface is tame if its complement is $1$-ULC, Trans. Amer. Math. Soc. 101 (1961), 294–305. MR 131265, DOI 10.1090/S0002-9947-1961-0131265-1
- 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, Approximating surfaces from the side, Ann. of Math. (2) 77 (1963), 145–192. MR 150744, DOI 10.2307/1970203
- R. H. Bing, Pushing a 2-sphere into its complement, Michigan Math. J. 11 (1964), 33–45. MR 160194
- Morton Brown, Locally flat imbeddings of topological manifolds, Ann. of Math. (2) 75 (1962), 331–341. MR 133812, DOI 10.2307/1970177
- C. E. Burgess, Characterizations of tame surfaces in $E^{3}$, Trans. Amer. Math. Soc. 114 (1965), 80–97. MR 176456, DOI 10.1090/S0002-9947-1965-0176456-2
- 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
- David S. Gillman, Side approximation, missing an arc, Amer. J. Math. 85 (1963), 459–476. MR 160193, DOI 10.2307/2373136
- O. G. Harrold Jr., Locally peripherally unknotted surfaces in $E^{3}$, Ann. of Math. (2) 69 (1959), 276–290. MR 105660, DOI 10.2307/1970182
- O. G. Harrold Jr., H. C. Griffith, and E. E. Posey, A characterization of tame curves in three-space, Trans. Amer. Math. Soc. 79 (1955), 12–34. MR 91457, DOI 10.1090/S0002-9947-1955-0091457-4
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- L. D. Loveland, Tame subsets of spheres in $E^{3}$, Pacific J. Math. 19 (1966), 489–517. MR 225309, DOI 10.2140/pjm.1966.19.489
- Edwin E. Moise, Affine structures in $3$-manifolds. VIII. Invariance of the knot-types; local tame imbedding, Ann. of Math. (2) 59 (1954), 159–170. MR 61822, DOI 10.2307/1969837
- R. L. Moore and J. R. Kline, On the most general plane closed point-set through which it is possible to pass a simple continuous arc, Ann. of Math. (2) 20 (1919), no. 3, 218–223. MR 1502556, DOI 10.2307/1967872
- G. T. Whyburn, Topological characterization of the Sierpiński curve, Fund. Math. 45 (1958), 320–324. MR 99638, DOI 10.4064/fm-45-1-320-324
Bibliographic Information
- © Copyright 1966 American Mathematical Society
- 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