A topological two-sphere in three-space whose exterior is not simply connected. The outer complement of Antoine's horned sphere is not simply connected. Furthermore, the group of the outer complement is not even finitely generated. Antoine's horned sphere is inequivalent to Alexander's horned sphere since the complement in of the bad points for Alexander's horned sphere is simply connected.
Antoine's Horned Sphere
See alsoAlexander's Horned Sphere
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ReferencesAlexander, J. W. "An Example of a Simply-Connected Surface Bounding a Region which is not Simply-Connected." Proc. Nat. Acad. Sci. 10, 8-10, 1924.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 76-79, 1976.
Referenced on Wolfram|AlphaAntoine's Horned Sphere
Cite this as:
Weisstein, Eric W. "Antoine's Horned Sphere." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AntoinesHornedSphere.html