# Homogeneous

From hyperspacewiki

A topological space $(X,\tau)$ is called homogeneous if for any $p,q \in X$ there exists a homeomorphism $h \colon Y \rightarrow Y$ such that $h(p)=q$.

# Examples

- a sphere is homogeneous (by rotation)
- topological groups are homogeneous (by translation)

# Properties

Characterization of when 2^X is homogeneous

Characterization of when C(X) is homogeneous