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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Invertibility in infinite-dimensional spaces


Authors: Chia-Chuan Tseng and Ngai-Ching Wong
Journal: Proc. Amer. Math. Soc. 128 (2000), 573-581
MSC (1991): Primary 46B20, 57N20, 57N50
Published electronically: July 6, 1999
MathSciNet review: 1628416
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Abstract: An interesting result of Doyle and Hocking states that a topological $n$-manifold is invertible if and only if it is a homeomorphic image of the $n$-sphere $S^n$. We shall prove that the sphere of any infinite-dimensional normed space is invertible. We shall also discuss the invertibility of other infinite-dimensional objects as well as an infinite-dimensional version of the Doyle-Hocking theorem.


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Additional Information

Chia-Chuan Tseng
Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan, Republic of China

Ngai-Ching Wong
Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan, Republic of China
Email: wong@math.nsysu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05076-5
PII: S 0002-9939(99)05076-5
Keywords: Invertible spaces, spheres, infinite-dimensional topology, infinite-dimensional manifolds
Received by editor(s): June 20, 1997
Received by editor(s) in revised form: April 14, 1998
Published electronically: July 6, 1999
Additional Notes: This work was partially supported by the National Science Council of Republic of China. Grant Number: NSC 83-0208-M-110-0171, 87-2115-M-110-002.
Communicated by: Dale Alspach
Article copyright: © Copyright 1999 American Mathematical Society