Shrinking decompositions of $E^{n}$ with countably many $1$-dimensional, star-like equivalent nondegenerate elements
HTML articles powered by AMS MathViewer
- by Terry L. Lay PDF
- Proc. Amer. Math. Soc. 79 (1980), 308-310 Request permission
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
- R. H. Bing, Upper semicontinuous decompositions of $E^3$, Ann. of Math. (2) 65 (1957), 363–374. MR 92960, DOI 10.2307/1969968
- 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 49549, DOI 10.2307/1969804
- Ralph J. Bean, Decompositions of $E^{3}$ with a null sequence of starlike equivalent non-degenerate elements are $E^{3}$, Illinois J. Math. 11 (1967), 21–23. MR 208581 R. D. Edwards, Approximating certain cell-like maps by homeomorphisms, Notices Amer. Math. Soc. 24 (1977), A-649.
- Michael Starbird and Edythe P. Woodruff, Decompositions of $E^{3}$ 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
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 308-310
- MSC: Primary 54B15; Secondary 57N37
- DOI: https://doi.org/10.1090/S0002-9939-1980-0565360-7
- MathSciNet review: 565360