Tame surfaces and tame subsets of spheres in

Author:
L. D. Loveland

Journal:
Trans. Amer. Math. Soc. **123** (1966), 355-368

MSC:
Primary 54.78

MathSciNet review:
0199850

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References | Similar Articles | Additional Information

**[1]**R. H. Bing,*Locally tame sets are tame*, Ann. of Math. (2)**59**(1954), 145–158. MR**0061377****[2]**R. H. Bing,*Approximating surfaces with polyhedral ones*, Ann. of Math. (2)**65**(1957), 465–483. MR**0087090****[3]**R. H. Bing,*An alternative proof that 3-manifolds can be triangulated*, Ann. of Math. (2)**69**(1959), 37–65. MR**0100841****[4]**R. H. Bing,*Conditions under which a surface in 𝐸³ is tame*, Fund. Math.**47**(1959), 105–139. MR**0107229****[5]**R. H. Bing,*A surface is tame if its complement is 1-ULC*, Trans. Amer. Math. Soc.**101**(1961), 294–305. MR**0131265**, 10.1090/S0002-9947-1961-0131265-1**[6]**R. H. Bing,*Each disk in 𝐸³ contains a tame arc*, Amer. J. Math.**84**(1962), 583–590. MR**0146811****[7]**R. H. Bing,*Each disk in 𝐸³ is pierced by a tame arc*, Amer. J. Math.**84**(1962), 591–599. MR**0146812****[8]**R. H. Bing,*Approximating surfaces from the side*, Ann. of Math. (2)**77**(1963), 145–192. MR**0150744****[9]**R. H. Bing,*Pushing a 2-sphere into its complement*, Michigan Math. J.**11**(1964), 33–45. MR**0160194****[10]**Morton Brown,*Locally flat imbeddings of topological manifolds*, Ann. of Math. (2)**75**(1962), 331–341. MR**0133812****[11]**C. E. Burgess,*Characterizations of tame surfaces in 𝐸³*, Trans. Amer. Math. Soc.**114**(1965), 80–97. MR**0176456**, 10.1090/S0002-9947-1965-0176456-2**[12]**P. H. Doyle and J. G. Hocking,*Some results on tame disks and spheres in 𝐸³*, Proc. Amer. Math. Soc.**11**(1960), 832–836. MR**0126839**, 10.1090/S0002-9939-1960-0126839-2**[13]**David S. Gillman,*Side approximation, missing an arc*, Amer. J. Math.**85**(1963), 459–476. MR**0160193****[14]**O. G. Harrold Jr.,*Locally peripherally unknotted surfaces in 𝐸³*, Ann. of Math. (2)**69**(1959), 276–290. MR**0105660****[15]**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**0091457**, 10.1090/S0002-9947-1955-0091457-4**[16]**Witold Hurewicz and Henry Wallman,*Dimension Theory*, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. MR**0006493****[17]**L. D. Loveland,*Tame subsets of spheres in 𝐸³*, Pacific J. Math.**19**(1966), 489–517. MR**0225309****[18]**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**0061822****[19]**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**, 10.2307/1967872**[20]**G. T. Whyburn,*Topological characterization of the Sierpiński curve*, Fund. Math.**45**(1958), 320–324. MR**0099638**

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DOI:
https://doi.org/10.1090/S0002-9947-1966-0199850-3

Article copyright:
© Copyright 1966
American Mathematical Society