Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Spheres in $ E\sp{3}$ 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

Abstract | References | Similar Articles | Additional Information

Abstract: A 2-sphere S in Euclidean 3-space $ {E^3}$ is defined to be homogeneous over the subset X of S if for each p, $ q \in X$ there is a homeomorphism $ h:{E^3} \to {E^3}$ such that $ h(S) = S$ and $ h(p) = q$. It is shown that a 2-sphere S in $ {E^3}$ 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.

References [Enhancements On Off] (What's this?)

  • [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 14, 192. MR 0049549 (14:192d)
  • [3] C. E. Burgess, Characterizations of tame surfaces in $ {E^3}$, Trans. Amer. Math. Soc. 114 (1965), 80-97. MR 31 #728. MR 0176456 (31:728)
  • [4] -, Embeddings of surfaces in Euclidean three-space, Bull. Amer. Math. Soc. 81 (1975), 795-818. MR 51 #11514. MR 0375319 (51:11514)
  • [5] C. E. Burgess and J. W. Cannon, Embeddings of surfaces in $ {E^3}$, Rocky Mountain J. Math. 1 (1971), 259-344. MR 43 #4008. MR 0278277 (43:4008)
  • [6] O. G. Harrold, Jr. and E. E. Moise, Almost locally polyhedral spheres, Ann. of Math. (2) 57 (1953), 575-578. MR 14 #784. MR 0053504 (14:784c)

Similar Articles

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

Retrieve articles in all journals with MSC: 57A10

Additional Information

Keywords: Tame spheres, homogeneous embeddings, horned spheres
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society