Locally convex linear topological spaces that are homeomorphic to the powers of the real line
HTML articles powered by AMS MathViewer
- by A. Chigogidze PDF
- Proc. Amer. Math. Soc. 113 (1991), 599-609 Request permission
Abstract:
We give a characterization of locally convex linear topological spaces that are homeomorphic to the uncountable powers of the real line.References
- Paul Alexandroff, Über nulldimensionale Punktmengen, Math. Ann. 98 (1928), no. 1, 89–106 (German). MR 1512393, DOI 10.1007/BF01451582
- Czesław Bessaga and Aleksander Pełczyński, Selected topics in infinite-dimensional topology, Monografie Matematyczne, Tom 58. [Mathematical Monographs, Vol. 58], PWN—Polish Scientific Publishers, Warsaw, 1975. MR 0478168
- A. Ch. Chigogidze, Noncompact absolute extensors in dimension $n,\;n$-soft mappings and their applications, Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), no. 1, 156–180, 208 (Russian). MR 835570
- A. Ch. Chigogidze, On the structure of nonmetrizable $\textrm {AE}(0)$-spaces, Mat. Zametki 41 (1987), no. 3, 406–411, 458 (Russian). MR 893369
- A. Ch. Chigogidze, Trivial bundles and near-homeomorphisms, Fund. Math. 132 (1989), no. 2, 89–98. MR 1002623, DOI 10.4064/fm-132-2-89-98
- A. N. Dranishnikov, Absolute extensors in dimension $n$ and $n$-soft mappings increasing the dimension, Uspekhi Mat. Nauk 39 (1984), no. 5(239), 55–95 (Russian). MR 764009
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- V. V. Fedorchuk, On open mappings, Uspekhi Mat. Nauk 37 (1982), no. 4(226), 187–188 (Russian). MR 667999
- Richard Haydon, On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim), Studia Math. 52 (1974), 23–31. MR 418025, DOI 10.4064/sm-52-1-23-31
- E. V. Ščepin, Functors and uncountable degrees of compacta, Uspekhi Mat. Nauk 36 (1981), no. 3(219), 3–62, 255 (Russian). MR 622720
- H. Toruńczyk, Characterizing Hilbert space topology, Fund. Math. 111 (1981), no. 3, 247–262. MR 611763, DOI 10.4064/fm-111-3-247-262
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 599-609
- MSC: Primary 46A03; Secondary 54A25, 57N17
- DOI: https://doi.org/10.1090/S0002-9939-1991-1064900-9
- MathSciNet review: 1064900