Tame surfaces and tame subsets of spheres in
Author:
L. D. Loveland
Journal:
Trans. Amer. Math. Soc. 123 (1966), 355368
MSC:
Primary 54.78
MathSciNet review:
0199850
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References 
Similar Articles 
Additional Information
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 [1]
 R. H. Bing, Locally tame sets are tame, Ann. of Math. 59 (1954), 145158. MR 0061377 (15:816d)
 [2]
 , Approximating surfaces with polyhedral ones, Ann. of Math. 65 (1957), 456483. MR 0087090 (19:300f)
 [3]
 , An alternative proof that manifolds can be triangulated, Ann. of Math. 69 (1959), 3765. MR 0100841 (20:7269)
 [4]
 , Conditions under which a surface in is tame, Fund. Math. 47 (1959), 105139. MR 0107229 (21:5954)
 [5]
 , A surface is tame if its complement is ULC, Trans. Amer. Math. Soc. 101 (1961), 294305. MR 0131265 (24:A1117)
 [6]
 , Each disk in contains a tame arc, Amer. J. Math. 84 (1962), 583590. MR 0146811 (26:4331)
 [7]
 , Each disk in is pierced by a tame arc, Amer. J. Math. 84 (1962), 591599. MR 0146812 (26:4332)
 [8]
 , Approximating surfaces from the side, Ann. of Math. 77 (1963), 145192. MR 0150744 (27:731)
 [9]
 , Pushing a sphere into its complement, Mich. Math. J. 11 (1964), 3345. MR 0160194 (28:3408)
 [10]
 Morton Brown, Locally flat imbeddings of topological manifolds, Ann. of Math. 75 (1962), 331341. MR 0133812 (24:A3637)
 [11]
 C. E. Burgess, Characterizations of tame surfaces in , Trans. Amer. Math. Soc. 114 (1965), 8097. MR 0176456 (31:728)
 [12]
 P. H. Doyle and J. G. Hocking, Some results on tame disks and spheres in , Proc. Amer. Math. Soc. 11 (1960), 832836. MR 0126839 (23:A4133)
 [13]
 D. S. Gillman, Side approximation, missing an arc, Amer. J. Math. 85 (1963), 459476. MR 0160193 (28:3407)
 [14]
 O. G. Harrold, Jr., Locally peripherally unknotted surfaces in , Ann. of Math. 69 (1959), 276290. MR 0105660 (21:4399a)
 [15]
 O. G. Harrold, Jr., H. C. Griffith, and E. E. Posey, A characterization of tame curves in space, Trans. Amer. Math. Soc. 79 (1955), 1235. 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 , Pacific J. Math. (to appear). MR 0225309 (37:903)
 [18]
 E. E. Moise, Affine structures in manifolds. VIII, Invariance of knottypes; local tame imbbeddings, Ann. of Math. 59 (1954), 159170. 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), 218223. MR 1502556
 [20]
 G. T. Whyburn, Topological characterization of the Sierpinski curve, Fund. Math. 45 (1958), 320324. MR 0099638 (20:6077)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947196601998503
PII:
S 00029947(1966)01998503
Article copyright:
© Copyright 1966
American Mathematical Society
