A surface is tame if its complement is -ULC

Author:
R. H. Bing

Journal:
Trans. Amer. Math. Soc. **101** (1961), 294-305

MSC:
Primary 54.75

DOI:
https://doi.org/10.1090/S0002-9947-1961-0131265-1

MathSciNet review:
0131265

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**[1]**J. W. Alexander,*An example of a simply connected surface bounding a region which is not simply connected*, Proc. Nat. Acad. Sci. U.S.A. vol. 10 (1924) pp. 8-10.**[2]**R. H. Bing,*Locally tame sets are tame*, Ann. of Math. vol. 59 (1954) pp. 145-158. MR**0061377 (15:816d)****[3]**-,*Approximating surfaces with polyhedral ones*, Ann. of Math. vol. 61 (1957) pp. 456-483.**[4]**-,*An alternative proof that*3-*manifolds can be triangulated*, Ann. of Math. vol. 69 (1959) pp. 37-65. MR**0100841 (20:7269)****[5]**-,*Conditions under which a surface in**is tame*, Fund. Math. vol. 47 (1959) pp. 105-139. MR**0107229 (21:5954)****[6]**-,*A wild sphere each of whose arcs is tame*, Duke Math. J.**[7]**-,*Side approximations of*2-*spheres*, submitted to Annals of Math.**[8]**R. H. Fox and E. Artin,*Some wild cells and spheres in three-dimensional space*, Ann. of Math. vol. 49 (1948) pp. 979-990. MR**0027512 (10:317g)****[9]**E. E. Moise,*Affine structures in*3-*manifolds*. IV.*Piecewise linear approximations of homeomorphisms*, Ann. of Math. vol. 55 (1952) pp. 215-222. MR**0046644 (13:765c)****[10]**-,*Affine structures in*3-*manifolds*, VIII.*Invariance of the knot-type*;*local tame imbedding*, Ann. of Math. vol. 59 (1954) pp. 159-170. MR**0061822 (15:889g)****[11]**C. D. Papakyriokopoulos,*On Dehn's lemma and the asphericity of knots*, Ann. of Math. vol. 66 (1957) pp. 1-26. MR**0090053 (19:761a)****[12]**J. R. Stallings,*Uncountably many wild disks*, Ann. of Math. vol. 71 (1960) pp. 185-186. MR**0111003 (22:1871)**

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DOI:
https://doi.org/10.1090/S0002-9947-1961-0131265-1

Article copyright:
© Copyright 1961
American Mathematical Society