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 Sphere## Explore 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 Sphere## Cite this as:

Weisstein, Eric W. "Antoine's Horned Sphere."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/AntoinesHornedSphere.html