A complete elementary proof that Hilbert space is homeomorphic to the countable infinite product of lines

Anderson, R. D.; Bing, R. H.

doi:10.1090/S0002-9904-1968-12044-0

A complete elementary proof that Hilbert space is homeomorphic to the countable infinite product of lines
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by R. D. Anderson and R. H. Bing PDF

Bull. Amer. Math. Soc. 74 (1968), 771-792

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, DOI 10.1307/mmj/1028999787
R. D. Anderson, On a theorem of Klee, Proc. Amer. Math. Soc. 17 (1966), 1401–1404. MR 205029, DOI 10.1090/S0002-9939-1966-0205029-4
C. Bessaga, On topological classification of complete linear metric spaces, Fund. Math. 56 (1964/65), 251–288. MR 178322, DOI 10.4064/fm-56-3-250-288
Czeslaw Bessaga and Victor Klee, Two topological properties of topological linear spaces, Israel J. Math. 2 (1964), 211–220. MR 180825, DOI 10.1007/BF02759736
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. MR 201949, DOI 10.1007/BF02052848
C. Bessaga and A. Pełczyński, Some remarks on homeomorphisms of $F$-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 265–270. MR 139917
M. Ĭ. Kadec′, Topological equivalence of all separable Banach spaces, Dokl. Akad. Nauk SSSR 167 (1966), 23–25 (Russian). MR 0201951
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). MR 0209804
Victor L. Klee Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10–43. MR 54850, DOI 10.1090/S0002-9947-1953-0054850-X
V. L. Klee Jr., Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 30–45. MR 69388, DOI 10.1090/S0002-9947-1955-0069388-5
V. L. Klee Jr., A note on topological properties of normed linear spaces, Proc. Amer. Math. Soc. 7 (1956), 673–674. MR 78661, DOI 10.1090/S0002-9939-1956-0078661-2

Additional Information

Journal: Bull. Amer. Math. Soc. 74 (1968), 771-792
DOI: https://doi.org/10.1090/S0002-9904-1968-12044-0
MathSciNet review: 0230284