Decompostions of with a compact dimensional set of nondegenerate elements
Author:
Steve Armentrout
Journal:
Trans. Amer. Math. Soc. 123 (1966), 165177
MSC:
Primary 54.78
MathSciNet review:
0195074
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References 
Similar Articles 
Additional Information
 [1]
Steve
Armentrout, Upper semicontinuous decompositions of 𝐸³
with at most countably many nondegenerate elements, Ann. of Math. (2)
78 (1963), 605–618. MR 0156331
(27 #6255)
 [2]
, Concerning pointlike decompositions of that yield manifolds, Abstract 619115, Notices Amer. Math. Soc. 12 (1965), 90.
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R. J. Bean, Decompositions of which yield , Abstract 619198, Notices Amer. Math. Soc. 12 (1965), 117.
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R.
H. Bing, Upper semicontinuous decompositions of
𝐸³, Ann. of Math. (2) 65 (1957),
363–374. MR 0092960
(19,1187f)
 [5]
R.
H. Bing, A decomposition of 𝐸³ into points and tame
arcs such that the decomposition space is topologically different from
𝐸³, Ann. of Math. (2) 65 (1957),
484–500. MR 0092961
(19,1187g)
 [6]
, A homeomorphism between the sphere and the sum of two solid horned spheres, Ann. of Math. 59 (1952), 354362.
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, Point like decompositions of , Fund. Math. 50 (1962), 431453.
 [8]
R.
H. Bing, Snakelike continua, Duke Math. J.
18 (1951), 653–663. MR 0043450
(13,265a)
 [9]
R.
H. Bing, Inequivalent families of periodic homeomorphisms of
𝐸³, Ann. of Math. (2) 80 (1964),
78–93. MR
0163308 (29 #611)
 [10]
, Topology of manifolds and related topics, Decompositions of , PrenticeHall, Englewood Cliffs, N.J., 1962; pp. 521.
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R.
H. Bing, An alternative proof that 3manifolds can be
triangulated, Ann. of Math. (2) 69 (1959),
37–65. MR
0100841 (20 #7269)
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K. W. Kwun, Upper semicontinuous decompositions of the sphere, Proc. Amer. Math. Soc. 13 (1962), 284290.
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Kyung
Whan Kwun and Frank
Raymond, Almost acyclic maps on manifolds, Amer. J. Math.
86 (1964), 638–650. MR 0184239
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L.L. Lininger, The sum of two crumpledcubes is if it is a manifold, Abstract 64T445, Notices Amer. Math. Soc. 11 (1964), 678.
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L. F. McAuley, Another decomposition of into points and intervals (to appear).
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Edwin
E. Moise, Affine structures in 3manifolds. V. The triangulation
theorem and Hauptvermutung, Ann. of Math. (2) 56
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L. Moore, Foundations of point set theory, Revised edition.
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D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of
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T. M. Price, Cellular decompositions of , Ph. D. Thesis, University of Wisconsin, Madison, Wis., 1964.
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Schubert, Knoten und Vollringe, Acta Math. 90
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G. Stewart, Cellular subsets of the
3sphere, Trans. Amer. Math. Soc. 114 (1965), 10–22. MR 0173244
(30 #3457), http://dx.doi.org/10.1090/S00029947196501732448
 [1]
 S. Armentrout, Upper semicontinuous decompositions of with at most countably many nondegenerate elements, Ann. of Math. 78 (1963), 605618. MR 0156331 (27:6255)
 [2]
 , Concerning pointlike decompositions of that yield manifolds, Abstract 619115, Notices Amer. Math. Soc. 12 (1965), 90.
 [3]
 R. J. Bean, Decompositions of which yield , Abstract 619198, Notices Amer. Math. Soc. 12 (1965), 117.
 [4]
 R. H. Bing, Upper semicontinuous decompositions of , Ann. of Math. 65 (1957), 363374. MR 0092960 (19:1187f)
 [5]
 , A decomposition of into points and tame arcs such that the decomposition space is topologically different from , Ann. of Math. 65 (1957), 484500. MR 0092961 (19:1187g)
 [6]
 , A homeomorphism between the sphere and the sum of two solid horned spheres, Ann. of Math. 59 (1952), 354362.
 [7]
 , Point like decompositions of , Fund. Math. 50 (1962), 431453.
 [8]
 , Snakelike continua, Duke Math. J. 18 (1951), 653663. MR 0043450 (13:265a)
 [9]
 , Inequivalent families of periodic homeomorphisms of , Ann. of Math. 80 (1964), 7893. MR 0163308 (29:611)
 [10]
 , Topology of manifolds and related topics, Decompositions of , PrenticeHall, Englewood Cliffs, N.J., 1962; pp. 521.
 [11]
 , An alternative proof that manifolds can be triangulated, Ann. of Math. 69 (1959), 3765. MR 0100841 (20:7269)
 [12]
 K. W. Kwun, Upper semicontinuous decompositions of the sphere, Proc. Amer. Math. Soc. 13 (1962), 284290.
 [13]
 K. W. Kwun and F. Raymond, Almost acyclic maps of manifolds, Amer. J. Math. 86 (1964), 638650. MR 0184239 (32:1712)
 [14]
 L.L. Lininger, The sum of two crumpledcubes is if it is a manifold, Abstract 64T445, Notices Amer. Math. Soc. 11 (1964), 678.
 [15]
 L. F. McAuley, Another decomposition of into points and intervals (to appear).
 [16]
 E. E. Moise, Affine structures in manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. 56 (1952), 92114. MR 0048805 (14:72d)
 [17]
 R. L. Moore, Foundations of point set theory, rev. ed., Amer. Math. Soc. Colloq. Publ. Vol. 13, Amer. Math. Soc., Providence, R. I., 1962, MR 0150722 (27:709)
 [18]
 C. D. Papakyriakopoulos, On Dehn's lemma and the asphericity of knots, Ann. of Math. 66 (1957), 1250. MR 0090053 (19:761a)
 [19]
 T. M. Price, Cellular decompositions of , Ph. D. Thesis, University of Wisconsin, Madison, Wis., 1964.
 [20]
 H. Schubert, Knoten und Vollringe, Acta Math. 90 (1953), 132286. MR 0072482 (17:291d)
 [21]
 D. G. Stewart, Cellular subsets of the sphere, Trans. Amer. Math. Soc. 114 (1965), 1022. MR 0173244 (30:3457)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947196601950744
PII:
S 00029947(1966)01950744
Article copyright:
© Copyright 1966
American Mathematical Society
