Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A topological proof of a theorem of Kneser


Author: Bjorn Friberg
Journal: Proc. Amer. Math. Soc. 39 (1973), 421-426
MSC: Primary 57E05
MathSciNet review: 0321124
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57E05

Retrieve articles in all journals with MSC: 57E05


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