Jordan-Brouwer separation theorem

This article describes a theorem about spheres

Statement

The Jordan-Brouwer separation theorem states that any subset of $S^{n}$ that is homeomorphic to $S^{n-1}$ must separate $S^{n}$ into two components, and must be precisely the common boundary between those two components.

The special case of this in two dimensions is the famous Jordan curve theorem.

Relation with other results

Related results

• Schoenflies theorem