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A complete elementary proof that Hilbert space is homeomorphic to the countable infinite product of lines. (English) Zbl 0189.12402


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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, On a theorem of Klee, Proc. Amer. Math. Soc. 17 (1966), 1401 – 1404. · Zbl 0152.12502
[5] S. Banach, Théorie des opérations linéaires, Monografie Mat. PWN, Warsaw, 1932. · JFM 58.0420.01
[6] C. Bessaga, On topological classification of complete linear metric spaces, Fund. Math. 56 (1964/1965), 251 – 288. · Zbl 0138.37404
[7] Czeslaw Bessaga and Victor Klee, Two topological properties of topological linear spaces, Israel J. Math. 2 (1964), 211 – 220. · Zbl 0138.37402 · doi:10.1007/BF02759736
[8] Czesław Bessaga and Victor Klee, Every non-normable Frechet space is homeomorphic with all of its closed convex bodies, Math. Ann. 163 (1966), 161 – 166. · Zbl 0138.37403 · doi:10.1007/BF02052848
[9] C. Bessaga and A. Pełczyński, Some remarks on homeomorphisms of \?-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 265 – 270. · Zbl 0103.32801
[10] M. Fréchet, Les espaces abstraits, Gauthier-Villars, Paris, 1928. · JFM 54.0614.02
[11] M. Ĭ. Kadec\(^{\prime}\), Topological equivalence of all separable Banach spaces, Dokl. Akad. Nauk SSSR 167 (1966), 23 – 25 (Russian).
[12] M. I. Kadec, A proof of the topological equivalence of all separable infinite-dimensional Banach spaces, Funkcional. Anal. i Priložen. 1 (1967), 61 – 70 (Russian). · Zbl 0166.10603
[13] Victor L. Klee Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10 – 43. · Zbl 0050.33202
[14] V. L. Klee Jr., Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 30 – 45. · Zbl 0064.10505
[15] V. L. Klee Jr., A note on topological properties of normed linear spaces, Proc. Amer. Math. Soc. 7 (1956), 673 – 674. · Zbl 0070.11103
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