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

 

Open subsets of $ R\sp{\infty }$ are stable


Author: Richard E. Heisey
Journal: Proc. Amer. Math. Soc. 59 (1976), 377-380
MSC: Primary 57A20; Secondary 58B05
MathSciNet review: 0425974
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Abstract: Let $ U$ be an open subset of $ {R^\infty } = \operatorname{dir} \lim {R^n}$, where $ R$ denotes the reals. We show that $ U \times {R^\infty }$ is homeomorphic to $ U$. Combined with previous work of the author we obtain the corollary that two open subsets of $ {R^\infty }$ are homeomorphic if and only if they have the same homotopy type.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0425974-0
PII: S 0002-9939(1976)0425974-0
Keywords: Open subset, direct limit, stability, homotopy type
Article copyright: © Copyright 1976 American Mathematical Society