Contractible Hilbert cube manifolds

Author:
T. A. Chapman

Journal:
Proc. Amer. Math. Soc. **35** (1972), 254-258

MSC:
Primary 58B05; Secondary 57A20

DOI:
https://doi.org/10.1090/S0002-9939-1972-0300313-0

MathSciNet review:
0300313

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Abstract: In this note we give an example of a contractible Hilbert cube manifold which cannot be embedded as an open subset of the Hilbert cube *Q* so that its complement (in *Q*) lies in a face of the boundary of *Q*. This example provides a negative answer to a question raised by the author.

**[1]**R. D. Anderson, T. A. Chapman and R. M. Schori,*Problems in the topology of infinite-dimensional spaces and manifolds*, ZW--report, Department of Pure Mathematics, Mathematical Center, Amsterdam, 1971.**[2]**R. H. Bing,*Necessary and sufficient conditions that a 3-manifold be 𝑆³*, Ann. of Math. (2)**68**(1958), 17–37. MR**0095471**, https://doi.org/10.2307/1970041**[3]**T. A. Chapman,*On the structure of Hilbert cube manifolds*, Compositio Math.**24**(1972), 329–353. MR**0305432****[4]**T. A. Chapman,*Hilbert cube manifolds*, Bull. Amer. Math. Soc.**76**(1970), 1326–1330. MR**0286138**, https://doi.org/10.1090/S0002-9904-1970-12660-X**[5]**T. A. Chapman,*On some applications of infinite-dimensional manifolds to the theory of shape*, Fund. Math.**76**(1972), no. 3, 181–193. MR**0320997**, https://doi.org/10.4064/fm-76-3-181-193**[6]**M. H. A. Newman and J. H. C. Whitehead,*On the group of a certain linkage*, Quart. J. Math.**8**(1937), 14-21.**[7]**J. H. C. Whitehead,*A certain open manifold whose group is unity*, Quart. J. Math.**6**(1935), 268-279.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0300313-0

Keywords:
Hilbert cube,
Hilbert cube manifold,
Whitehead's example

Article copyright:
© Copyright 1972
American Mathematical Society