Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Some imbedding and nonimbedding theorems for $ n$-manifolds


Author: Beauregard Stubblefield
Journal: Trans. Amer. Math. Soc. 103 (1962), 403-420
MSC: Primary 54.78
DOI: https://doi.org/10.1090/S0002-9947-1962-0143189-5
MathSciNet review: 0143189
Full-text PDF

References | Similar Articles | Additional Information

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

  • [1] R. H. Bing, A decomposition of $ {E^3}$ into points and tame arcs such that the decomposition space is topologically different from $ {E^3}$, Ann. of Math. 65 (1957), 484-500. MR 0092961 (19:1187g)
  • [2] -, The Cartesian product of a certain nonmanifold and a line is $ {E^4}$, Bull. Amer. Math. Soc. 64 (1958), 82-84. MR 0097034 (20:3514)
  • [3] K. Borsuk, On the decomposition of a locally connected compactum into Cartesian product of a curve and a manifold, Fund. Math. 40 (1953), 140-159. MR 0061819 (15:889d)
  • [4] W. W. S. Claytor, Topological immersion of Peanian continua in a spherical surface, Ann. of Math. 35 (1934), 809-835. MR 1503198
  • [5] -, Peano continua not imbeddable in a spherical surface, Ann. of Math. 38 (1937), 631-646.
  • [6] R. H. Fox, On a problem of S. Ulam concerning Cartesian products, Fund. Math. 34 (1947), 278-287. MR 0027502 (10:316a)
  • [7] F. B. Jones and G. S. Young, Product spaces in n-manifolds, Proc. Amer. Math. Soc. 10 (1959), 307-308. MR 0105662 (21:4400)
  • [8] E. E. Moise, An indecomposable plane continuum which is homeomorphic to each of its nondegenerate subcontinua, Trans. Amer. Math. Soc. 63 (1948), 581-594. MR 0025733 (10:56i)
  • [9] -, Remarks on the Claytor imbedding theorem, Duke Math. J. 19 (1952), 199-202. MR 0050879 (14:396f)
  • [10] E. E. Moise and G. S. Young, On imbedding continuous curves in 2-manifolds, Bull. Amer. Math. Soc. 54 (1948), 77.
  • [11] R. L. Moore, Concerning triods in the plane and the junction points of plane continua Proc. Nat. Acad. Sci. U.S.A. 14 (1928), 85-88.
  • [12] J. H. C. Whitehead, On the homotopy type of manifolds, Ann. of Math. 41 (1940), 825. MR 0002546 (2:73e)
  • [13] G. S. Young, Jr., A generalization of Moore's theorem on simple triods, Bull. Amer. Math. Soc. 50 (1944), 714. MR 0010967 (6:96c)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54.78

Retrieve articles in all journals with MSC: 54.78


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1962-0143189-5
Article copyright: © Copyright 1962 American Mathematical Society

American Mathematical Society