Bing's example
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This article is about Bing's theorem on the Cartesian product of topological spaces. For Bing's metrization theorem, see Bing metrization theorem.
In topology, Bing's theorem asserts that there exists a topological space F which is not a manifold, but such that the Cartesian product F×R with the real line is homeomorphic to R4. In particular, this shows that the Cartesian product of a manifold with a non-manifold may still be a manifold. The result is not true for differentiable manifolds, however.
[edit] References
- Bing, R.H. (1959). "The Cartesian product of a certain nonmanifold and a line is E4". Annals of Mathematics 70 (3): 399–412. doi:.
- Epstein, D. and Thurston, W. (1979). "Transformation groups and natural bundles". Proc. London Math. Soc. 38 (3): 219–236. doi:.
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