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Recent classification and characterization results in geometric topology
Author(s):
J. J.
Dijkstra;
T.
Dobrowolski;
W.
Marciszewski;
J.
van Mill;
J.
Mogilski
Journal:
Bull. Amer. Math. Soc.
22
(1990),
277-283.
MSC (1985):
Primary 57N15, 57N20
MathSciNet review:
1027899
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References:
- 1.
- R. D. Anderson, Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 72 (1966), 515-519. MR 190888
- 2.
- R. D. Anderson, Strongly negligible sets in Fréchet manifolds, Bull. Amer. Math. Soc. 75 (1969), 64-67. MR 238358
- 3.
- A. V. Arhangel'skiĭ, A survey of C, Questions Answers Gen. Topology 5 (1987), 1-109. MR 909494
- 4.
- A. V. Arhangel'skiĭ, Some results and problems in C(X)-theory, Proc. Sixth Prague Topological Sympos., Heldermann, Berlin, 1988, pp. 11-31. MR 952587
- 5.
- J. Baars, J. de Groot, J. van Mill, and J. Pelant, On topological and linear homeomorphisms of certain function spaces, Topology Appl. 32 (1989), 267-277. MR 1007105
- 6.
- S. Banach, Théorie des Opérations Linéaires, PWN, Warsaw, 1932.
- 7.
- C. Bessaga and A. Pelczyński, Selected topics in infinite-dimensional topology, PWN, Warsaw, 1975. MR 478168
- 8.
- M. Bestvina and J. Mogilski, Characterizing certain incomplete infinite-dimensional absolute retracts, Michigan Math. J. 33 (1986), 291-313. MR 856522
- 9.
- J. J. Dijkstra, Fake topological Hilbert spaces and characterizations of dimension in terms of negligibility, CWI Tracts vol. 2, Centre for Math, and Comp. Sci., Amsterdam, 1984. MR 753464
- 10.
- J. J. Dijkstra, k-Dimensional skeletoids in R, Topology Appl. 19 (1985), 13-28. MR 786078
- 11.
- J. J. Dijkstra, Strong negligibility of σ-compacta does not characterize Hilbert space, Pacific J. Math. 127 (1987), 19-30. MR 876016
- 12.
- J. J. Dijkstra, Characterizing Hilbert space topology in terms of strong negligibility, preprint. MR 1070416
- 13.
- J. J. Dijkstra, J. van Mill, and J. Mogilski, Classification of finite-dimensional universal pseudoboundaries and pseudointeriors, Trans. Amer. Math. Soc. (to appear). MR 1052905
- 14.
- J. J. Dijkstra, T. Grilliot, D. Lutzer, and J. van Mill, Function spaces of low Borel complexity, Proc. Amer. Math. Soc. 94 (1985), 703-710. MR 792287
- 15.
- T. Dobrowolski and J. Mogilski, Certain sequence and function spaces homeomorphic to the countable product of $\ell\sp{2}\sbf$, preprint.
- 16.
- T. Dobrowolski, S. P. Gulko, and J. Mogilski, Function spaces homeomorphic to the countable product of $\ell \sp f\sb 2$, Topology Appl. (to appear). MR 1041769
- 17.
- T. Dobrowolski, W. Marciszewski, and J. Mogilski, On topological classification of function spaces C(X) of low Borel complexity, preprint. MR 1065602
- 18.
- M. Fréchet, Les espaces abstraits, Hermann, Paris, 1928.
- 19.
- R. Geoghegan and R. R. Summerhill, Concerning the shapes of finite-dimensional compacta, Trans. Amer. Math. Soc. 179 (1973), 281-292. MR 324637
- 20.
- R. Geoghegan and R. R. Summerhill, Pseudoboundaries and pseudointeriors in euclidean spaces and topological manifolds, Trans. Amer. Math. Soc. 194 (1974), 141-165. MR 356061
- 21.
- M. I. Kadec, A proof of topological equivalence of all separable infinite-dimensional Banach spaces (Russian), Funkcional. Anal. i Prilozen. 1 (1967), 53-62. MR 209804
- 22.
- J. van Mill, Topological equivalence of certain function spaces, Compositio Math. 63(1987), 159-188. MR 906368
- 23.
- J. van Mill, Infinite-dimensional Topology: Prerequisites and introduction, North-Holland, Amsterdam, 1989. MR 977744
- 24.
- J. Mogilski, Characterizing the topology of infinite-dimensional σ-compact manifolds, Proc. Amer. Math. Soc. 92 (1984), 111-118. MR 749902
- 25.
- H. Toruńczyk, Characterizing Hilbert space topology, Fund. Math. 111 (1981), 247-262. MR 611763
- 26.
- H. Toruńczyk, A correction of two papers concerning Hilbert manifolds, Fund. Math. 125 (1985), 89-93. MR 813992
- 27.
- J. E. West, The ambient homeomorphy of an incomplete subspace of infinite-dimensional Hilbert spaces, Pacific J. Math. 34 (1970), 257-267. MR 277011
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Additional Information:
DOI:
10.1090/S0273-0979-1990-15887-2
PII:
S 0273-0979(1990)15887-2
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