Invertibility in infinite-dimensional spaces

Tseng, Chia-Chuan; Wong, Ngai-Ching

doi:10.1090/S0002-9939-99-05076-5

Invertibility in infinite-dimensional spaces
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by Chia-Chuan Tseng and Ngai-Ching Wong

Proc. Amer. Math. Soc. 128 (2000), 573-581

DOI: https://doi.org/10.1090/S0002-9939-99-05076-5

Published electronically: July 6, 1999

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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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