The union of two Hilbert cubes meeting in a Hilbert cube need not be a Hilbert cube
HTML articles powered by AMS MathViewer
- by R. B. Sher PDF
- Proc. Amer. Math. Soc. 63 (1977), 150-152 Request permission
Abstract:
An example is given to verify the assertion of the title.References
- R. D. Anderson, Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc. 126 (1967), 200β216. MR 205212, DOI 10.1090/S0002-9947-1967-0205212-3
- R. D. Anderson, On topological infinite deficiency, Michigan Math. J. 14 (1967), 365β383. MR 214041
- 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), 771β792. MR 230284, DOI 10.1090/S0002-9904-1968-12044-0
- R. D. Anderson and T. A. Chapman, Extending homeomorphisms to Hilbert cube manifolds, Pacific J. Math. 38 (1971), 281β293. MR 319204
- R. D. Anderson and Nelly Kroonenberg, Open problems in infinite-dimensional topology, Topological structures (Proc. Sympos. in honour of Johannes de Groot (1914-1972), Amsterdam, 1973) Math. Centre Tracts, No. 52, Math. Centrum, Amsterdam, 1974, pp.Β 141β175. MR 0358788
- R. H. Bing, A homeomorphism between the $3$-sphere and the sum of two solid horned spheres, Ann. of Math. (2) 56 (1952), 354β362. MR 49549, DOI 10.2307/1969804
- William A. Blankinship, Generalization of a construction of Antoine, Ann. of Math. (2) 53 (1951), 276β297. MR 40659, DOI 10.2307/1969543
- Robert J. Daverman, On the scarcity of tame disks in certain wild cells, Fund. Math. 79 (1973), no.Β 1, 63β77. MR 326742, DOI 10.4064/fm-79-1-63-77
- 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 Mike Handel, On certain sums of Hilbert cubes (to appear).
- Raymond Y. T. Wong, A wild Cantor set in the Hilbert cube, Pacific J. Math. 24 (1968), 189β193. MR 221487
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 150-152
- MSC: Primary 57A20; Secondary 54F99
- DOI: https://doi.org/10.1090/S0002-9939-1977-0645402-0
- MathSciNet review: 0645402