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Shrinking decompositions of $ E\sp{n}$ with countably many $ 1$-dimensional, star-like equivalent nondegenerate elements


Author: Terry L. Lay
Journal: Proc. Amer. Math. Soc. 79 (1980), 308-310
MSC: Primary 54B15; Secondary 57N37
MathSciNet review: 565360
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Abstract: It is shown that an upper semicontinuous decomposition of $ {E^n}(n \geqslant 1)$ with countably many 1-dimensional, star-like equivalent nondegenerate elements is shrinkable.


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

  • [Bi 1] R. H. Bing, Upper semicontinuous decompositions of 𝐸³, Ann. of Math. (2) 65 (1957), 363–374. MR 0092960
  • [Bi 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
  • [Be] Ralph J. Bean, Decompositions of 𝐸³ with a null sequence of starlike equivalent non-degenerate elements are 𝐸³, Illinois J. Math. 11 (1967), 21–23. MR 0208581
  • [Ed] R. D. Edwards, Approximating certain cell-like maps by homeomorphisms, Notices Amer. Math. Soc. 24 (1977), A-649.
  • [S-W] Michael Starbird and Edythe P. Woodruff, Decompositions of 𝐸³ with countably many nondegenerate elements, Geometric topology (Proc. Georgia Topology Conf., Athens, Ga., 1977), Academic Press, New York-London, 1979, pp. 239–252. MR 537733

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0565360-7
Keywords: Upper semicontinuous decomposition, shrinkable decomposition, shrinkability criterion, star-like equivalent
Article copyright: © Copyright 1980 American Mathematical Society