Spheres in which are homogeneous over a 0-dimensional set

Author:
C. E. Burgess

Journal:
Proc. Amer. Math. Soc. **63** (1977), 171-174

MSC:
Primary 57A10

MathSciNet review:
0442942

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A 2-sphere *S* in Euclidean 3-space is defined to be homogeneous over the subset *X* of *S* if for each *p*, there is a homeomorphism such that and . It is shown that a 2-sphere *S* in is tame from one side provided *S* is locally tame modulo a tame 0-dimensional set *C* such that *S* is homogeneous over *C*. An example is described to show that it is necessary to require that *C* be tame.

**[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.**10**(1924), 8-10.**[2]**R. H. Bing,*A homeomorphism between the 3-sphere and the sum of two solid horned spheres*, Ann. of Math. (2)**56**(1952), 354–362. MR**0049549****[3]**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**[4]**C. E. Burgess,*Embeddings of surfaces in Euclidean three-space*, Bull. Amer. Math. Soc.**81**(1975), no. 5, 795–818. MR**0375319**, 10.1090/S0002-9904-1975-13834-1**[5]**C. E. Burgess and J. W. Cannon,*Embeddings of surfaces in 𝐸³*, Rocky Mountain J. Math.**1**(1971), no. 2, 259–344. MR**0278277****[6]**O. G. Harrold Jr. and E. E. Moise,*Almost locally polyhedral spheres*, Ann. of Math. (2)**57**(1953), 575–578. MR**0053504**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
57A10

Retrieve articles in all journals with MSC: 57A10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0442942-4

Keywords:
Tame spheres,
homogeneous embeddings,
horned spheres

Article copyright:
© Copyright 1977
American Mathematical Society