Bing's recognition theorem explained

In topology, a branch of mathematics, Bing's recognition theorem, named for R. H. 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. It is a weak version of the Poincaré conjecture.

References

• Bing. R. H.. Necessary and sufficient conditions that a 3-manifold be . Annals of Mathematics. Second Series. 1958. 68. 1. 10.2307/1970041. 17–37. 0081.39202. 0095471. R. H. Bing.
• Book: 0415619. 3-Manifolds. Hempel. John. John Hempel. Annals of Mathematics Studies. 86. Princeton University Press. Princeton, NJ. 1976. 0345.57001. 10.1090/chel/349.
• Book: 1277811. Knots and links. Rolfsen. Dale. Mathematics Lecture Series. 7. Publish or Perish, Inc.. Houston, TX. 1990. 0-914098-16-0. 0854.57002. Corrected reprint of the 1976 original. 10.1090/chel/346.