Bing's Theorem
If M^3 is a closed oriented connected 3-manifold such that every simple closed curve in M lies interior to a ball in M, then M is homeomorphic with the hypersphere, S^3.
See also
Ball, HypersphereExplore with Wolfram|Alpha
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References
Bing, R. H. "Necessary and Sufficient Conditions that a 3-Manifold be S^3." Ann. Math. 68, 17-37, 1958.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 251-257, 1976.Referenced on Wolfram|Alpha
Bing's TheoremCite this as:
Weisstein, Eric W. "Bing's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BingsTheorem.html