# sphere theorem

> theorem stating that a complete, simply-connected, n-dimensional Riemannian manifold with sectional curvature taking values in the interval (1, 4] is homeomorphic to the n-sphere

**Wikidata**: [Q2309682](https://www.wikidata.org/wiki/Q2309682)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Sphere_theorem)  
**Source**: https://4ort.xyz/entity/sphere-theorem