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)

 
 

 

Spheroidal decompostions of $ E\sp{4}$


Author: J. P. Neuzil
Journal: Trans. Amer. Math. Soc. 155 (1971), 35-64
MSC: Primary 54.78
DOI: https://doi.org/10.1090/S0002-9947-1971-0273587-6
MathSciNet review: 0273587
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper investigates a generalization to $ {E^4}$ of the notion of toroidal decomposition of $ {E^3}$. A certain type of this kind of upper semicontinuous decomposition is shown to be shrinkable and hence yield $ {E^4}$ as its decomposition space.


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

  • [1] S. Armentrout and R. H. Bing, A toroidal decomposition of $ {E^3}$, Fund. Math. 60 (1967), 81-87. MR 34 #6741. MR 0206925 (34:6741)
  • [2] R. H. Bing, Upper semicontinuous decompositions of $ {E^3}$, Ann. of Math. (2) 65 (1957), 363-374. MR 19, 1187. MR 0092960 (19:1187f)
  • [3] -, Point-like decompositions of $ {E^3}$, Fund. Math. 50 (1961/62), 431-453. MR 25 #560. MR 0137104 (25:560)
  • [4] J. F. P. Hudson, Piecewise linear topology, Benjamin, New York, 1969. MR 0248844 (40:2094)
  • [5] L. L. Lininger, Actions on $ {S^n}$ (to appear).
  • [6] R. B. Sher, Toroidal decompositions of $ {E^3}$, Fund. Math. 61 (1967/68), 225-241. MR 37 #905. MR 0225311 (37:905)

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/S0002-9947-1971-0273587-6
Keywords: Simple spheroidal decomposition, spheroidal decomposition, point-like decompostion, toroidal decomposition, upper semicontinuous decomposition, decomposition spaces, Euclidean $ 4$-space
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society