Glasnik Matematicki, Vol. 46, No. 2 (2011), 483-487.

CORRECTING TAYLOR'S CELL-LIKE MAP

Katsuro Sakai

Abstract.   J. L. Taylor constructed a cell-like map of a compactum X onto the Hilbert cube I^N such that X is not cell-like. In this note, we point out a defect in the construction and show how to fix it.

2000 Mathematics Subject Classification.   54C10, 54C56, 55P40, 57N25.

Key words and phrases.   Taylor's cell-like map, Hilbert cube, n-fold suspension.

DOI: 10.3336/gm.46.2.16

References:

1. J. F. Adams, On the groups J(X). IV, Topology 5 (1966), 21-71; errata, ibid. 7 (1968), 331.
   MathSciNet     CrossRef
   MathSciNet     CrossRef

2. C. Bessaga and A. Pełczyński, Selected topics in infinite-dimensional topology, Monografie Matematyczne 58, PWN Polish Scientific Publishers, Warsaw, 1975.
   MathSciNet    

3. Z. Čerin, Characterizing global properties in inverse limits, Pacific J. Math. 112 (1984), 49-68.
   MathSciNet     CrossRef

4. O.-H. Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931), 748-758.
   MathSciNet     CrossRef

5. S. Mardešić and J. Segal, Shape theory. The inverse system approach, North-Holland Mathematical Library 26, North-Holland Publishing Co., Amsterdam-New York, 1982.
   MathSciNet    

6. J. van Mill, Infinite-dimensional topology. Prerequisites and introduction, North-Holland Mathematical Library 43, North-Holland Publishing Co., Amsterdam, 1989.
   MathSciNet    

7. J. L. Taylor, A counterexample in shape theory, Bull. Amer. Math. Soc. 81 (1975), 629-632.
   MathSciNet     CrossRef

8. H. Toruńczyk, On CE-images of the Hilbert cube and characterization of Q-manifolds, Fund. Math. 106 (1980), 31-40.
   MathSciNet    

9. J. J. Walsh, Characterization of Hilbert cube manifolds: an alternate proof, in: Geometric and algebraic topology, Banach Center Publ. 18, PWN Polish Scientific Publishers, Warsaw, 1986, 153-160.
   MathSciNet