Bulletin (New Series) of the American Mathematical Society

Recent classification and characterization results in geometric topology

J. J. Dijkstra, T. Dobrowolski, W. Marciszewski, J. van Mill, and J. Mogilski

Full-text: Open access

Article information

Bull. Amer. Math. Soc. (N.S.), Volume 22, Number 2 (1990), 277-283.

First available in Project Euclid: 4 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N15: Topology of $E^n$ , $n$-manifolds ($4 \less n \less \infty$) 57N20: Topology of infinite-dimensional manifolds [See also 58Bxx]


Dijkstra, J. J.; Dobrowolski, T.; Marciszewski, W.; van Mill, J.; Mogilski, J. Recent classification and characterization results in geometric topology. Bull. Amer. Math. Soc. (N.S.) 22 (1990), no. 2, 277--283. https://projecteuclid.org/euclid.bams/1183555622

Export citation


  • 1. R. D. Anderson, Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 72 (1966), 515-519.
  • 2. R. D. Anderson, Strongly negligible sets in Fréchet manifolds, Bull. Amer. Math. Soc. 75 (1969), 64-67.
  • 3. A. V. Arhangel'skiĭ, A survey of Cp-theory, Questions Answers Gen. Topology 5 (1987), 1-109.
  • 4. A. V. Arhangel'skiĭ, Some results and problems in Cp(X)-theory, Proc. Sixth Prague Topological Sympos., Heldermann, Berlin, 1988, pp. 11-31.
  • 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.
  • 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.
  • 8. M. Bestvina and J. Mogilski, Characterizing certain incomplete infinite-dimensional absolute retracts, Michigan Math. J. 33 (1986), 291-313.
  • 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.
  • 10. J. J. Dijkstra, k-Dimensional skeletoids in Rn and the Hilbert cube, Topology Appl. 19 (1985), 13-28.
  • 11. J. J. Dijkstra, Strong negligibility of σ-compacta does not characterize Hilbert space, Pacific J. Math. 127 (1987), 19-30.
  • 12. J. J. Dijkstra, Characterizing Hilbert space topology in terms of strong negligibility, preprint.
  • 13. J. J. Dijkstra, J. van Mill, and J. Mogilski, Classification of finite-dimensional universal pseudoboundaries and pseudointeriors, Trans. Amer. Math. Soc. (to appear).
  • 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.
  • 15. T. Dobrowolski and J. Mogilski, Certain sequence and function spaces homeomorphic to the countable product of $l^2_f$, preprint.
  • 16. T. Dobrowolski, S. P. Gulko, and J. Mogilski, Function spaces homeomorphic to the countable product of $l^2_f$, Topology Appl. (to appear).
  • 17. T. Dobrowolski, W. Marciszewski, and J. Mogilski, On topological classification of function spaces Cp(X) of low Borel complexity, preprint.
  • 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.
  • 20. R. Geoghegan and R. R. Summerhill, Pseudoboundaries and pseudointeriors in euclidean spaces and topological manifolds, Trans. Amer. Math. Soc. 194 (1974), 141-165.
  • 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.
  • 22. J. van Mill, Topological equivalence of certain function spaces, Compositio Math. 63(1987), 159-188.
  • 23. J. van Mill, Infinite-dimensional Topology: Prerequisites and introduction, North-Holland, Amsterdam, 1989.
  • 24. J. Mogilski, Characterizing the topology of infinite-dimensional σ-compact manifolds, Proc. Amer. Math. Soc. 92 (1984), 111-118.
  • 25. H. Toruńczyk, Characterizing Hilbert space topology, Fund. Math. 111 (1981), 247-262.
  • 26. H. Toruńczyk, A correction of two papers concerning Hilbert manifolds, Fund. Math. 125 (1985), 89-93.
  • 27. J. E. West, The ambient homeomorphy of an incomplete subspace of infinite-dimensional Hilbert spaces, Pacific J. Math. 34 (1970), 257-267.