Topological equivalence of certain function spaces

J. Van Mill

Compositio Mathematica (1987)

  • Volume: 63, Issue: 2, page 159-188
  • ISSN: 0010-437X

How to cite


Van Mill, J.. "Topological equivalence of certain function spaces." Compositio Mathematica 63.2 (1987): 159-188. <>.

author = {Van Mill, J.},
journal = {Compositio Mathematica},
keywords = {Hilbert cube; isotopy; N-skeleton; pointwise convergence; Hilbert space},
language = {eng},
number = {2},
pages = {159-188},
publisher = {Martinus Nijhoff Publishers},
title = {Topological equivalence of certain function spaces},
url = {},
volume = {63},
year = {1987},

AU - Van Mill, J.
TI - Topological equivalence of certain function spaces
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 63
IS - 2
SP - 159
EP - 188
LA - eng
KW - Hilbert cube; isotopy; N-skeleton; pointwise convergence; Hilbert space
UR -
ER -


  1. 1 R.D. Anderson: On topological infinite deficiency. Mich. Math. J.14 (1967) 365-383. Zbl0148.37202MR214041
  2. 2 R.D. Anderson: On sigma-compact subsets of infinite-dimensional spaces. Unpublished manuscript. 
  3. 3 A.V. Arhangelskii: The principle of τ-approximation and a test for equality of dimension of compact Hausdorff spaces. Soviet Math. Dokl.21 (1980) 805-809. Zbl0491.54028
  4. 4 A.V. Arhangelskii: On linear homeomorphisms of function spaces. Soviet Math. Dokl.25 (1982) 852-855. Zbl0522.54015
  5. 5 C. Bessaga and A. Pelczyński: Spaces of continuous functions (IV) (On isomorphical classification of function spaces C(S)). Studia Math.19 (1960) 53-62. Zbl0094.30303MR113132
  6. 6 C. Bessaga and A. Pelczyński: Selected topics in infinite-dimensional topology. PWN, Warsaw (1975). Zbl0304.57001MR478168
  7. 7 K. Borsuk: Theory of retracts. PWN, Warsaw (1967). Zbl0153.52905MR216473
  8. 8 T.A. Chapman: Dense sigma-compact subsets of infinite-dimensional manifolds. Trans. Amer. Math. Soc.154 (1971) 399-426. Zbl0208.51903MR283828
  9. 9 T.A. Chapman: Lectures on Hilbert cube manifolds. CMBS Regional Conf. Series in Math. no. 28. Amer. Math. Soc., Providence, R.I. (1976). Zbl0347.57005MR423357
  10. 10 J.J. Dijkstra: Fake topological Hilbert spaces and characterizations of dimension in terms of negligibility. CWI Tract2. Amsterdam, (1984). Zbl0543.57001MR753464
  11. 11 J.J. Dijkstra, T. Grilliot, D.J. Lutzer and J. van Mill: Function spaces of low Borel complexity. Proc. Amer. Math. Soc.94 (1985) 703-710. Zbl0525.54010MR792287
  12. 12 F. van Engelen: Characterization of the countable infinite product of rationals and some related problems. To appear. Zbl0642.54033MR897969
  13. 13 R. Engelking: On closed images of the space of irrationals. Proc. Amer. Math. Soc.21 (1969) 583-586. Zbl0177.25501MR239571
  14. 14 D.J. Lutzer, J. van Mill and R. Pol: Descriptive complexity of function spaces. Trans. Amer. Math. Soc.291 (1985) 121-128. Zbl0574.54042MR797049
  15. 15 J. Mogilski: Characterizing the topology of infinite-dimensional σ-compact manifolds. Proc. Amer. Math. Soc.92 (1984) 111-118. Zbl0577.57005
  16. 16 S. Negrepontis: Banach spaces and topology, Handbook of Set theoretic Topology, (K. Kunen and J.E. Vaughan, eds.). North-Holland (1984) 1045-1142. Zbl0584.46007MR776642
  17. 17 D. Pavlovskii: On spaces of continuous functions. Soviet Math. Dokl.22 (1980) 34-37. Zbl0489.54011MR577006
  18. 18 Z. Semadeni: Banach spaces of continuous functions. PWN, Warsaw (1971). Zbl0225.46030
  19. 19 J.R. Steel: Analytic sets and Borel isomorphisms. Fund. Math.108 (1980) 83-88. Zbl0463.03028MR594307
  20. 20 H. ToruńczykOn cartesian factors and the topological classification of linear metric spaces. Fund. Math.88 (1975) 71-86. Zbl0308.57004MR391102
  21. 21 H. Toruńczyk: On CE-images of the Hilbert cube and characterization of Q-manifolds. Fund. Math.108 (1980) 31-40. Zbl0346.57004MR585543
  22. 22 H. Toruńczyk: Characterizing Hilbert space topology. Fund. Math.111 (1981) 247-262. Zbl0468.57015MR611763
  23. 23 H. Toruńczyk: (G,K)-absorbing and skeletonized sets in metric spaces. Diss. Math. (to appear). Zbl0202.54003
  24. 24 J.E. West: The ambient homeomorphy of an incomplete subspace of infinite-dimensional Hilbert spaces. Pacific J. Math.34 (1970) 257-267. Zbl0198.46001MR277011

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