Union of convex Hilbert cubes
HTML articles powered by AMS MathViewer
- by J. Quinn and Raymond Y. T. Wong
- Proc. Amer. Math. Soc. 65 (1977), 171-176
- DOI: https://doi.org/10.1090/S0002-9939-1977-0500981-9
- PDF | Request permission
Abstract:
We show that the finite union of Keller cubes in a Hilbert space is homeomorphic to the Hilbert cube provided every subcollection intersects in a Hilbert cube.References
- R. D. Anderson, Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc. 126 (1967), 200–216. MR 205212, DOI 10.1090/S0002-9947-1967-0205212-3 —, A characterization of apparent boundaries of the Hilbert cube, Notices Amer. Math. Soc. 16 (1969), 429. Abstract #69T-G17.
- 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), 771–792. MR 230284, DOI 10.1090/S0002-9904-1968-12044-0
- 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. 141–175. MR 0358788
- Czesław Bessaga and Aleksander Pełczyński, Selected topics in infinite-dimensional topology, Monografie Matematyczne, Tom 58. [Mathematical Monographs, Vol. 58], PWN—Polish Scientific Publishers, Warsaw, 1975. MR 0478168
- T. A. Chapman, Hilbert cube manifolds, Bull. Amer. Math. Soc. 76 (1970), 1326–1330. MR 286138, DOI 10.1090/S0002-9904-1970-12660-X
- T. A. Chapman, On the structure of Hilbert cube manifolds, Compositio Math. 24 (1972), 329–353. MR 305432 Michael Handel, The Bing staircase construction for Hilbert cube manifolds (submitted). —, On certain sums of Hilbert cubes (submitted).
- Nelly Kroonenberg, Characterization of finite-dimensional $Z$-sets, Proc. Amer. Math. Soc. 43 (1974), 421–427. MR 334221, DOI 10.1090/S0002-9939-1974-0334221-8
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- S. Nadler Jr., J. Quinn, and N. M. Stavrakas, Hyperspaces of compact convex sets. I, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 23 (1975), no. 5, 555–559 (English, with Russian summary). MR 420535 —, Hyperspaces of compact convex sets. II, Bull. Polon. Acad. Sci. (to appear).
- Sam B. Nadler Jr., J. Quinn, and Nick M. Stavrakas, Hyperspaces of compact convex sets, Pacific J. Math. 83 (1979), no. 2, 441–462. MR 557944 R. Sher, The union of two Hilbert cubes meeting in a Hilbert cube need not be a Hilbert cube (submitted).
- J. E. West, Identifying Hilbert cubes: general methods and their application to hyperspaces by Schori and West, General topology and its relations to modern analysis and algebra, III (Proc. Third Prague Topological Sympos., 1971) Academia, Prague, 1972, pp. 455–461. MR 0353236
- James E. West, Infinite products which are Hilbert cubes, Trans. Amer. Math. Soc. 150 (1970), 1–25. MR 266147, DOI 10.1090/S0002-9947-1970-0266147-3
- Raymond Y. T. Wong and Nelly Kroonenberg, Unions of Hilbert cubes, Trans. Amer. Math. Soc. 211 (1975), 289–297. MR 377895, DOI 10.1090/S0002-9947-1975-0377895-3
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 171-176
- MSC: Primary 57A20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0500981-9
- MathSciNet review: 0500981