Conditions for a TVS to be homeomorphic with its countable product
HTML articles powered by AMS MathViewer
- by Wesley E. Terry
- Trans. Amer. Math. Soc. 190 (1974), 233-242
- DOI: https://doi.org/10.1090/S0002-9947-1974-0338725-8
- PDF | Request permission
Abstract:
C. Bessaga has given conditions for a Banach space to be homeomorphic with its countable product. In this paper, we extend and generalize these results to complete metric topological vector spaces by using infinite dimensional techniques.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, Strongly negligible sets in Fréchet manifolds, Bull. Amer. Math. Soc. 75 (1969), 64–67. MR 238358, DOI 10.1090/S0002-9904-1969-12146-4
- 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, David W. Henderson, and James E. West, Negligible subsets of infinite-dimensional manifolds, Compositio Math. 21 (1969), 143–150. MR 246326
- 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
- William H. Cutler, Negligible subsets of infinite-dimensional Fréchet manifolds, Proc. Amer. Math. Soc. 23 (1969), 668–675. MR 248883, DOI 10.1090/S0002-9939-1969-0248883-5 M. Eidelheit and S. Mazur, Eine Bemerkung über die Räume vom Typus (F), Studia Math. 7 (1938), 159-161.
- David W. Henderson and R. Schori, Topological classification of infinite dimensional manifolds by homotopy type, Bull. Amer. Math. Soc. 76 (1970), 121–124. MR 251749, DOI 10.1090/S0002-9904-1970-12392-8
- J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. MR 0166578, DOI 10.1007/978-3-662-41914-4
- Ernest Michael, Convex structures and continuous selections, Canadian J. Math. 11 (1959), 556–575. MR 109344, DOI 10.4153/CJM-1959-051-9
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210528
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 190 (1974), 233-242
- MSC: Primary 46A15; Secondary 58B05
- DOI: https://doi.org/10.1090/S0002-9947-1974-0338725-8
- MathSciNet review: 0338725