A general class of factors of
Author:
Leonard R. Rubin
Journal:
Trans. Amer. Math. Soc. 166 (1972), 215224
MSC:
Primary 57A15
Erratum:
Trans. Amer. Math. Soc. 177 (1973), 505.
MathSciNet review:
0295314
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Abstract: In this paper we prove that any upper semicontinuous decomposition of which is generated by a trivial defining sequence of cubes with handles determines a factor of . An important corollary to this result is that every 0dimensional pointlike decomposition of determines a factor of . In our approach we have simplified the construction of the sequence of shrinking homeomorphisms by eliminating the necessity of shrinking sets piecewise in a collection of ncells, the technique employed by R. H. Bing in the original result of this type.
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 [1]
 W. R. Alford and R. B. Sher, Defining sequences for compact 0dimensional decompositions of , Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 17 (1969), 209212. MR 40 #8031. MR 0254824 (40:8031)
 [2]
 J. J. Andrews and M. L. Curtis, nspace modulo an arc, Ann. of Math. (2) 75 (1962), 17. MR 25 #2590. MR 0139153 (25:2590)
 [3]
 J. J. Andrews and Leonard Rubin, Some spaces whose product with is , Bull. Amer. Math. Soc. 71 (1965), 675677. MR 31 #726. MR 0176454 (31:726)
 [4]
 R. H. Bing, A decomposition of into points and tame arcs such that the decomposition space is topologically different from , Ann. of Math. (2) 65 (1957), 484500. MR 19, 1187. MR 0092961 (19:1187g)
 [5]
 , The cartesian product of a certain nonmanifold and a line is , Ann. of Math. (2) 70 (1959), 399412. MR 21 #5953. MR 0107228 (21:5953)
 [6]
 , Pointlike decompositions of , Fund. Math. 50 (1961/62), 431453. MR 25 #560. MR 0137104 (25:560)
 [7]
 J. L. Bryant, Euclidean space modulo a cell, Fund. Math. 63 (1968), 4351. MR 37 #5861. MR 0230298 (37:5861)
 [8]
 , Euclidean nspace modulo an cell (to appear).
 [9]
 J. Dugundji, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 33 #1824. MR 0193606 (33:1824)
 [10]
 R. C. Lacher, Celllike mappings. I, Pacific J. Math. 30 (1969), 717731. MR 40 #4941. MR 0251714 (40:4941)
 [11]
 H. W. Lambert and R. B. Sher, Pointlike 0dimensional decompositions of , Pacific J. Math. 24 (1968), 511518. MR 37 #902. MR 0225308 (37:902)
 [12]
 D. R. McMillan, Jr., A criterion for cellularity in a manifold, Ann. of Math. (2) 79 (1964), 327337. MR 28 #4528. MR 0161320 (28:4528)
 [13]
 R. H. Rosen, is the Cartesian product of a totally noneuclidean space and , Ann. of Math. (2) 73 (1961), 349361. MR 23 #A2198. MR 0124888 (23:A2198)
 [14]
 L. R. Rubin, The product of an unusual decomposition space with a line is , Duke Math. J. 33 (1966), 323329. MR 33 #3283. MR 0195078 (33:3283)
 [15]
 , The product of any dogbone space with a line is , Duke Math. J. 37 (1970), 189192. MR 0267548 (42:2450)
 [16]
 , Recognizing certain factors of , Proc. Amer. Math. Soc. 26 (1970), 199200. MR 42 #1088. MR 0266180 (42:1088)
 [17]
 E. H. Spanier, Algebraic topology, McGrawHill, New York, 1966. MR 35 #1007. MR 0210112 (35:1007)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719720295314X
PII:
S 00029947(1972)0295314X
Keywords:
Cubes with handles,
defining sequence,
trivial defining sequence,
universal covering space,
0dimensional decomposition,
pointlike decomposition,
celllike spaces,
property UV
Article copyright:
© Copyright 1972
American Mathematical Society
