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Invertibility in infinite-dimensional spaces |
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| Authors: | Chia-Chuan Tseng Ngai-Ching Wong |
| Institution: | Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan, Republic of China Ngai-Ching Wong ; Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan, Republic of China |
| 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. |
| Keywords: | Invertible spaces spheres infinite-dimensional topology infinite-dimensional manifolds |
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