Contracting spaces of maps on the countable direct limit of a space
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- by Richard E. Heisey PDF
- Trans. Amer. Math. Soc. 193 (1974), 389-411 Request permission
Abstract:
We give conditions sufficient to imply the contractibility of the space of maps, with compact-open topology, on the countable direct limit of a space. Applying these conditions we obtain the following: Let F be the conjugate of a separable infinite-dimensional Banach space with bounded weak-$^\ast$ topology, or the countable direct limit of the real line. Then there is a contraction of the space of maps on F which simultaneously contracts the subspaces of open maps, embeddings, closed embeddings, and homeomorphisms. Corollaries of our work are that any homeomorphism on F, F as above, is invertibly isotopic to the identity, and the general linear group of the countable direct limit of lines is contractible.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 193 (1974), 389-411
- MSC: Primary 54C35
- DOI: https://doi.org/10.1090/S0002-9947-1974-0367908-6
- MathSciNet review: 0367908