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A topological proof of a theorem of Kneser


Author: Bjorn Friberg
Journal: Proc. Amer. Math. Soc. 39 (1973), 421-426
MSC: Primary 57E05
DOI: https://doi.org/10.1090/S0002-9939-1973-0321124-7
MathSciNet review: 0321124
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Abstract: We give an elementary topological proof that the orthogonal groups $ O(2)$ and $ O(3)$ are strong deformation retracts of the space of homeomorphisms (with the compact-open topology) of $ {R^2}$ and $ {S^2}$, respectively. We also deform the space of bounded homeomorphisms of $ {R^2}$ to $ {S^1}$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0321124-7
Keywords: Homeomorphism, deformation, isotopy, topological group, bounded homeomorphism
Article copyright: © Copyright 1973 American Mathematical Society

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