Homogeneous

From hyperspacewiki
Jump to: navigation, search

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

  1. a sphere is homogeneous (by rotation)
  2. topological groups are homogeneous (by translation)

Properties

Characterization of when 2^X is homogeneous
Characterization of when C(X) is homogeneous