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Extending monotone decompositions of 3-manifolds. (English) Zbl 0205.53401

##### MSC:
 57N10 Topology of general $$3$$-manifolds (MSC2010) 57N12 Topology of the Euclidean $$3$$-space and the $$3$$-sphere (MSC2010) 54B15 Quotient spaces, decompositions in general topology
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##### References:
 [1] R. H. Bing, A characterization of 3-space by partitionings, Trans. Amer. Math. Soc. 70 (1951), 15 – 27. · Zbl 0042.41903 [2] R. H. Bing, Concerning hereditarily indecomposable continua, Pacific J. Math. 1 (1951), 43 – 51. · Zbl 0043.16803 [3] R. H. Bing, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145 – 158. · Zbl 0055.16802 · doi:10.2307/1969836 · doi.org [4] R. H. Bing, An alternative proof that 3-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37 – 65. · Zbl 0106.16604 · doi:10.2307/1970092 · doi.org [5] -, “Decompositions of $${E^3}$$” in Topology of 3-manifolds and related topics (Proc. Univ. of Georgia Institute, 1961), Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 5-21. MR 25 #4501. [6] B. G. Casler, An imbedding theorem for connected 3-manifolds with boundary, Proc. Amer. Math. Soc. 16 (1965), 559 – 566. · Zbl 0129.15801 [7] J. F. P. Hudson and E. C. Zeeman, On regular neighbourhoods, Proc. London Math. Soc. (3) 14 (1964), 719 – 745. · Zbl 0123.39601 · doi:10.1112/plms/s3-14.4.719 · doi.org [8] Edwin E. Moise, Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 56 (1952), 96 – 114. · Zbl 0048.17102 · doi:10.2307/1969769 · doi.org [9] Edwin E. Moise, Affine structures in 3-manifolds. VIII. Invariance of the knot-types; local tame imbedding, Ann. of Math. (2) 59 (1954), 159 – 170. · Zbl 0055.16804 · doi:10.2307/1969837 · doi.org [10] J. H. C. Whitehead, Simplicial spaces, nuclei, and m-groups, Proc. London Math. Soc. (2), 45 (1939), 243-327. · Zbl 0022.40702 [11] G. T. Whyburn, Decomposition spaces, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 2 – 4. · Zbl 1246.57004 [12] E. C. Zeeman, Polyhedral \?-manifolds. II. Embeddings, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 65 – 70. · Zbl 1246.57064
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