{{Short description|On when a 3-manifold is homeomorphic to the 3-sphere}} In topology, a branch of mathematics, '''Bing's recognition theorem''', named for R. H. Bing, asserts that a necessary and sufficient condition for a {{nowrap|3-manifold}} ''M'' to be homeomorphic to the {{nowrap|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== * {{cite journal|last=Bing|first=R. H.|title=Necessary and sufficient conditions that a 3-manifold be {{math|''S''<sup>3</sup>}}|journal=Annals of Mathematics|series=Second Series|year=1958|volume=68|issue=1|doi=10.2307/1970041|pages=17–37|zbl=0081.39202|mr=0095471|author-link1=R. H. Bing}} {{erratum|doi=10.2307/1970205|checked=yes}} * {{cite book|mr=0415619|title=3-Manifolds|last1=Hempel|first1=John|author-link1=John Hempel|series=Annals of Mathematics Studies|volume=86|publisher=Princeton University Press|location=Princeton, NJ|year=1976|zbl=0345.57001|doi=10.1090/chel/349}} * {{cite book|mr=1277811|title=Knots and links|last1=Rolfsen|first1=Dale|series=Mathematics Lecture Series|volume=7|publisher=Publish or Perish, Inc.|location=Houston, TX|year=1990|isbn=0-914098-16-0|zbl=0854.57002|edition=Corrected reprint of the 1976 original|doi=10.1090/chel/346}} {{topology-stub}} Category:3-manifolds Category:Geometric topology Category:Theorems in topology