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

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

MathSciNet review:
0199850

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References | Similar Articles | Additional Information

**[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 -manifolds can be triangulated*, Ann. of Math.**69**(1959), 37-65. MR**0100841 (20:7269)****[4]**-,*Conditions under which a surface in is tame*, Fund. Math.**47**(1959), 105-139. MR**0107229 (21:5954)****[5]**-,*A surface is tame if its complement is*-ULC, Trans. Amer. Math. Soc.**101**(1961), 294-305. MR**0131265 (24:A1117)****[6]**-,*Each disk in contains a tame arc*, Amer. J. Math.**84**(1962), 583-590. MR**0146811 (26:4331)****[7]**-,*Each disk in 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 -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*, 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*, 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*, 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 -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*, Pacific J. Math. (to appear). MR**0225309 (37:903)****[18]**E. E. Moise,*Affine structures in -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