The union of two Hilbert cubes meeting in a Hilbert cube need not be a Hilbert cube
Author:
R. B. Sher
Journal:
Proc. Amer. Math. Soc. 63 (1977), 150152
MSC:
Primary 57A20; Secondary 54F99
MathSciNet review:
0645402
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: An example is given to verify the assertion of the title.
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 [1]
 R. D. Anderson, Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc. 126 (1967), 200216. MR 34 #5045. MR 0205212 (34:5045)
 [2]
 , On topological infinite deficiency, Michigan Math. J. 14 (1967), 365383. MR 35 #4893. MR 0214041 (35:4893)
 [3]
 R. D. Anderson and R. H. Bing, A complete elementary proof that Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 74 (1968), 771792. MR 37 #5847. MR 0230284 (37:5847)
 [4]
 R. D. Anderson and T. A. Chapman, Extending homeomorphisms to Hilbert cube manifolds, Pacific J. Math. 38 (1971), 281293. MR 47 #7749. MR 0319204 (47:7749)
 [5]
 R. D. Anderson and Nelly Kroonenberg, Open problems in infinitedimensional topology, Math. Centre Tracts, no. 52, Mathematisch Centrum, Amsterdam, 1974, pp. 141175. MR 0358788 (50:11247)
 [6]
 R. H. Bing, A homeomorphism between the 3sphere and the sum of two solid horned spheres, Ann. of Math. (2) 56 (1952), 354362. MR 14, 192. MR 0049549 (14:192d)
 [7]
 William A. Blankinship, Generalization of a construction of Antoine, Ann. of Math. (2) 53 (1951), 276297. MR 12,730. MR 0040659 (12:730c)
 [8]
 Robert J. Daverman, On the scarcity of tame disks in certain wild cells, Fund. Math. 79 (1973), 6377. MR 48 #5085. MR 0326742 (48:5085)
 [9]
 W. T. Eaton, A generalization of the dog bone space to , Proc. Amer. Math. Soc. 39 (1973), 379387. MR 48 #1238. MR 0322877 (48:1238)
 [10]
 Mike Handel, On certain sums of Hilbert cubes (to appear).
 [11]
 Raymond Y. T. Wong, A wild Cantor set in the Hilbert cube, Pacific J. Math. 24 (1968), 189193. MR 36 #4539. MR 0221487 (36:4539)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197706454020
PII:
S 00029939(1977)06454020
Keywords:
Hilbert cube,
dogbone decomposition,
Zset
Article copyright:
© Copyright 1977
American Mathematical Society
