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 also
Alexander's Horned SphereExplore with Wolfram|Alpha
References
Alexander, 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|Alpha
Antoine's Horned SphereCite this as:
Weisstein, Eric W. "Antoine's Horned Sphere." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AntoinesHornedSphere.html