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Dense sigma-compact subsets of infinite-dimensional manifolds. (English) Zbl 0208.51903


MSC:

58B05 Homotopy and topological questions for infinite-dimensional manifolds
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[1] R. D. Anderson, Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 72 (1966), 515 – 519. · Zbl 0137.09703
[2] R. D. Anderson, Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc. 126 (1967), 200 – 216. · Zbl 0152.12601
[3] R. D. Anderson, On topological infinite deficiency, Michigan Math. J. 14 (1967), 365 – 383. · Zbl 0148.37202
[4] R. D. Anderson, Strongly negligible sets in Fréchet manifolds, Bull. Amer. Math. Soc. 75 (1969), 64 – 67. · Zbl 0195.53602
[5] -, A characterization of apparent boundaries of the Hilbert cube, Notices Amer. Math. Soc. 16 (1969), 429. Abstract #697-G17.
[6] -, On sigma-compact subsets of infinite-dimensional spaces, Trans. Amer. Math. Soc. (submitted).
[7] 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. · Zbl 0189.12402
[8] R. D. Anderson and John D. McCharen, On extending homeomorphisms to Fréchet manifolds, Proc. Amer. Math. Soc. 25 (1970), 283 – 289. · Zbl 0203.25805
[9] R. D. Anderson and R. Schori, Factors of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 142 (1969), 315 – 330. · Zbl 0187.20505
[10] R. D. Anderson, David W. Henderson, and James E. West, Negligible subsets of infinite-dimensional manifolds, Compositio Math. 21 (1969), 143 – 150. · Zbl 0185.50803
[11] William Barit, Small extensions of small homeomorphisms, Notices Amer. Math. Soc. 16 (1969), 295. Abstract #663-715.
[12] 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). · Zbl 0204.12801
[13] T. A. Chapman, Infinite deficiency in Fréchet manifolds, Trans. Amer. Math. Soc. 148 (1970), 137 – 146. · Zbl 0194.55601
[14] David W. Henderson, Infinite-dimensional manifolds are open subsets of Hilbert space, Bull. Amer. Math. Soc. 75 (1969), 759 – 762. · Zbl 0179.29101
[15] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. · Zbl 0060.39808
[16] K. Kuratowski, Topologie. Vol. 1: Espaces métrisables, espaces complets, 2nd ed., Monografie Mat., Tom 20, PWN, Warsaw, 1948. MR 10, 389.
[17] 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 Loose Russian summary). · Zbl 0202.54003
[18] James E. West, Infinite products which are Hilbert cubes, Trans. Amer. Math. Soc. 150 (1970), 1 – 25. · Zbl 0198.56001
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