Open subsets of $R^{\infty }$ are stable
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- by Richard E. Heisey PDF
- Proc. Amer. Math. Soc. 59 (1976), 377-380 Request permission
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.References
- Richard E. Heisey, Contracting spaces of maps on the countable direct limit of a space, Trans. Amer. Math. Soc. 193 (1974), 389–411. MR 367908, DOI 10.1090/S0002-9947-1974-0367908-6
- Richard E. Heisey, Manifolds modelled on $R^{\infty }$ or bounded weak-* topologies, Trans. Amer. Math. Soc. 206 (1975), 295–312. MR 397768, DOI 10.1090/S0002-9947-1975-0397768-X
- C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972. MR 0350744, DOI 10.1007/978-3-642-81735-9
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 377-380
- MSC: Primary 57A20; Secondary 58B05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0425974-0
- MathSciNet review: 0425974