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Bing's recognition theorem

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This article is about Bing's theorem on 3-manifolds. For Bing's metrization theorem, see Bing metrization theorem. For Bing's example of a product of non-manifolds, see Bing's example.

In topology, Bing's theorem, named for RH Bing, asserts that a necessary and sufficient condition for a 3-manifold M to be homeomorphic to the 3-sphere is that every Jordan curve in M be contained within a topological ball.

References

  • Bing, RH (1958). "Necessary and sufficient condition that the 3-manifold be S3". Annals of Mathematics. 68 (1): 17. doi:10.2307/1970041.
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