Characterizing infinite dimensional manifolds topologically

Robert D. Edwards

Séminaire Bourbaki (1978-1979)

  • Volume: 21, page 278-302
  • ISSN: 0303-1179

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Edwards, Robert D.. "Characterizing infinite dimensional manifolds topologically." Séminaire Bourbaki 21 (1978-1979): 278-302. <http://eudml.org/doc/109941>.

@article{Edwards1978-1979,
author = {Edwards, Robert D.},
journal = {Séminaire Bourbaki},
keywords = {Hilbert cube manifold characterization; Hilbert space manifold characterization; approximation by homeomorphisms; absolute neighbourhood retracts; mapping cylinder neighbourhood theorem},
language = {eng},
pages = {278-302},
publisher = {Springer-Verlag},
title = {Characterizing infinite dimensional manifolds topologically},
url = {http://eudml.org/doc/109941},
volume = {21},
year = {1978-1979},
}

TY - JOUR
AU - Edwards, Robert D.
TI - Characterizing infinite dimensional manifolds topologically
JO - Séminaire Bourbaki
PY - 1978-1979
PB - Springer-Verlag
VL - 21
SP - 278
EP - 302
LA - eng
KW - Hilbert cube manifold characterization; Hilbert space manifold characterization; approximation by homeomorphisms; absolute neighbourhood retracts; mapping cylinder neighbourhood theorem
UR - http://eudml.org/doc/109941
ER -

References

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  1. [An1] R.D. Anderson - Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc.126(1967), 200-216. Announced in Bull. Amer. Math. Soc.72(1966), 515-519. See also [A-B]. Zbl0152.12601MR205212
  2. [An2] R.D. Anderson - On topological infinite deficiency, Michigan Math. J.14(1967), 365-383. Zbl0148.37202MR214041
  3. [An3] R.D. Anderson - Strongly negligible sets in Fréchet manifolds, Bull. Amer. Math. Soc.75(1969), 64-67. Zbl0195.53602MR238358
  4. [An4] R.D. Anderson - Homeomorphisms on infinite-dimensional manifolds, Actes, Congrès International des Mathématiciens, Nice1970, Tome 2, 13-18. Zbl0228.57007MR454983
  5. [A-B] R.D. Anderson and R.H. Bing - A completely elementary proof that Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc.74(1968), 771-792. Zbl0189.12402MR230284
  6. [Bi] R.H. Bing - A homeomorphism between the 3-sphere and the sum of two solid horned spheres, Annals of Math.56(1952), 354-362. Zbl0049.40401MR49549
  7. [Ch1] T.A. Chapman - Cell-like mappings of Hilbert cube manifolds : Solution of a handle problem, General Top. and Appl.5(1975), 123-145. Zbl0308.58002MR377894
  8. [Ch2] T.A. Chapman - Lectures on Hilbert Cube Manifolds, Regional Conference Series in Mathematics n° 28, Amer. Math. Soc.1976. Zbl0347.57005MR423357
  9. [C-S] D.W. Curtis and R.M. Schori - 2X and C(X) are homeomorphic to the Hilbert cube, Bull. Amer. Math. Soc.80(1974), 927-931. Zbl0302.54011MR353235
  10. [Ed] R.D. Edwards - The ANR Theorem, Chapter 14 in [Ch2]. 
  11. [Hat] A.E. Hatcher - Higher simple homotopy theory, Annals of Math.102(1975), 101-137. Zbl0305.57009MR383424
  12. [Hav] W.E. Haver - Mappings between ANR's that are fine homotopy equivalences, Pacific Jour. Math.58(1975), 457-461. Zbl0311.55006MR385865
  13. [Hu] S.-T. Hu - Theory of Retracts, Wayne State University Press, 1965. Zbl0145.43003MR181977
  14. [La] R.C. Lacher - Cell-like mappings, I, Pacific Jour. Math.30(1969), 717-731. Zbl0182.57601MR251714
  15. [Mi] R.T. Miller - Mapping cylinder neighborhoods of some ANR's, Annals of Math. 103(1976), 417-427. Announced in Bull. Amer. Math. Soc.81(1975), 187-188. Zbl0296.54015MR358790
  16. [S-W] R.M. Schori and J.E. West - The hyperspace of the closed unit interval is a Hilbert cube, Trans. Amer. Math. Soc.213(1975), 217-235. Announced in Bull. Amer. Math. Soc.79(1973), 1286-1291. Zbl0312.54011MR390993
  17. [To1] H. Toruńczyk - Absolute retracts as factors of normed linear spaces, Fund. Math.86(1974), 53-67. Zbl0318.57005MR365471
  18. [To2] H. Toruńczyk - On CE-images of the Hilbert cube and characterization of Q-manifolds, Fund. Math., to appear. Zbl0346.57004MR585543
  19. [To3] H. Toruńczyk - Characterizing Hilbert space topology, Preprint 143, Institute of Mathematics, Polish Academy of Sciences, 1978. MR611763
  20. [To4] H. Toruńczyk - An Introduction to Infinite-Dimensional Topology, in preparation. 
  21. [We] J.E. West - Mapping Hilbert cube manifolds to ANR's : a solution of a conjecture of Borsuk, Annals of Math.106(1977), 1-18. Announced in Bull. Amer. Math. Soc.81(1975), 163-165. Zbl0375.57013MR451247

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