A nonshrinkable decomposition of $S^{n}$ determined by a null sequence of cellular sets
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- by Robert J. Daverman PDF
- Proc. Amer. Math. Soc. 75 (1979), 171-176 Request permission
Abstract:
The result derived is one of existence: there is a decomposition of the n-sphere ${S^n}(n \geqslant 5)$ into points and a null sequence of cellular sets that is not shrinkable. In one form the implicit example leads to a nonmanifold decomposition space closely allied with the nonmanifold βdogboneβ space developed by W. T. Eaton.References
- Steve Armentrout, $\textrm {UV}$ properties of compact sets, Trans. Amer. Math. Soc. 143 (1969), 487β498. MR 273573, DOI 10.1090/S0002-9947-1969-0273573-7
- Steve Armentrout, Cellular decompositions of $3$-manifolds that yield $3$-manifolds, Memoirs of the American Mathematical Society, No. 107, American Mathematical Society, Providence, R.I., 1971. MR 0413104 F. D. Ancel, The locally flat approximation of cell-like embedding relations, Doctoral thesis, Univ. of Wisconsin at Madison, 1976.
- 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. (2) 65 (1957), 484β500. MR 92961, DOI 10.2307/1970058 β, Point-like decompositions of ${E^3}$, Fund. Math. 50 (1962), 431-453.
- R. H. Bing and Michael Starbird, A decomposition of $S^{3}$ with a null sequence of cellular arcs, Geometric topology (Proc. Georgia Topology Conf., Athens, Ga., 1977) Academic Press, New York-London, 1979, pp.Β 3β21. MR 537722 R. J. Daverman, Sewings of closed n-cell-complements, Trans. Amer. Math. Soc. (to appear).
- W. T. Eaton, A generalization of the dog bone space to $E^{n}$, Proc. Amer. Math. Soc. 39 (1973), 379β387. MR 322877, DOI 10.1090/S0002-9939-1973-0322877-4 R. D. Edwards, Approximating certain cell-like maps by homeomorphisms, (manuscript); see Notices Amer. Math. Soc. 24 (1977), A-649, #751-G5. D. S. Gillman and J. M. Martin, Countable decompositions of ${E^3}$ into points and point-like arcs, Notices Amer. Math. Soc. 10 (1963), 74.
- Robion C. Kirby, On the set of non-locally flat points of a submanifold of codimension one, Ann. of Math. (2) 88 (1968), 281β290. MR 236900, DOI 10.2307/1970575
- R. C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83 (1977), no.Β 4, 495β552. MR 645403, DOI 10.1090/S0002-9904-1977-14321-8
- D. R. McMillan Jr., A criterion for cellularity in a manifold, Ann. of Math. (2) 79 (1964), 327β337. MR 161320, DOI 10.2307/1970548
- L. C. Siebenmann, Approximating cellular maps by homeomorphisms, Topology 11 (1972), 271β294. MR 295365, DOI 10.1016/0040-9383(72)90014-6 M. Starbird, Null sequence cellular decompositions of ${S^3}$ (to appear).
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 171-176
- MSC: Primary 57N15; Secondary 54B15, 57N60
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529236-5
- MathSciNet review: 529236