Dense sigma-compact subsets of infinite-dimensional manifolds
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- by T. A. Chapman
- Trans. Amer. Math. Soc. 154 (1971), 399-426
- DOI: https://doi.org/10.1090/S0002-9947-1971-0283828-7
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Abstract:
In this paper four classes of separable metric infinite-dimensional manifolds are studied; those which are locally the countable infinite product of lines, those which are locally open subsets of the Hubert cube, and those which are locally one of two dense sigma-compact subsets of the Hilbert cube. A number of homeomorphism, product, characterization, and embedding theorems are obtained concerning these manifolds.References
- R. D. Anderson, Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 72 (1966), 515–519. MR 190888, DOI 10.1090/S0002-9904-1966-11524-0
- 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
- R. D. Anderson, On topological infinite deficiency, Michigan Math. J. 14 (1967), 365–383. MR 214041
- R. D. Anderson, Strongly negligible sets in Fréchet manifolds, Bull. Amer. Math. Soc. 75 (1969), 64–67. MR 238358, DOI 10.1090/S0002-9904-1969-12146-4 —, A characterization of apparent boundaries of the Hilbert cube, Notices Amer. Math. Soc. 16 (1969), 429. Abstract #697-G17. —, On sigma-compact subsets of infinite-dimensional spaces, Trans. Amer. Math. Soc. (submitted).
- 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 John D. McCharen, On extending homeomorphisms to Fréchet manifolds, Proc. Amer. Math. Soc. 25 (1970), 283–289. MR 258064, DOI 10.1090/S0002-9939-1970-0258064-5
- R. D. Anderson and R. Schori, Factors of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 142 (1969), 315–330. MR 246327, DOI 10.1090/S0002-9947-1969-0246327-5
- R. D. Anderson, David W. Henderson, and James E. West, Negligible subsets of infinite-dimensional manifolds, Compositio Math. 21 (1969), 143–150. MR 246326 William Barit, Small extensions of small homeomorphisms, Notices Amer. Math. Soc. 16 (1969), 295. Abstract #663-715. C. Bessaga and A. Pełczyński, Estimated extension theorem, homogeneous collections and skeletons, and their applications to topological classifications of linear metric spaces and convex sets, Fund. Math. (submitted).
- T. A. Chapman, Infinite deficiency in Fréchet manifolds, Trans. Amer. Math. Soc. 148 (1970), 137–146. MR 256418, DOI 10.1090/S0002-9947-1970-0256418-9
- David W. Henderson, Infinite-dimensional manifolds are open subsets of Hilbert space, Bull. Amer. Math. Soc. 75 (1969), 759–762. MR 247634, DOI 10.1090/S0002-9904-1969-12276-7
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493 K. Kuratowski, Topologie. Vol. 1: Espaces métrisables, espaces complets, 2nd ed., Monografie Mat., Tom 20, PWN, Warsaw, 1948. MR 10, 389.
- H. Toruńczyk, Skeletonized sets in complete metric spaces and homeomorphisms of the Hilbert cube, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 119–126 (English, with Russian summary). MR 264602
- 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
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 154 (1971), 399-426
- MSC: Primary 57.55
- DOI: https://doi.org/10.1090/S0002-9947-1971-0283828-7
- MathSciNet review: 0283828