Proceedings of the American Mathematical Society

Author(s): Chia-Chuan Tseng; Ngai-Ching Wong
Journal: Proc. Amer. Math. Soc. 128 (2000), 573-581.
MSC (1991): Primary 46B20, 57N20, 57N50
Posted: July 6, 1999
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Abstract: An interesting result of Doyle and Hocking states that a topological

-manifold is invertible if and only if it is a homeomorphic image of the

-sphere

. 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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46B20, 57N20, 57N50

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: 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
Posted: 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
Copyright of article: Copyright 1999, American Mathematical Society

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