In algebraic topology, a branch of mathematics, a simple space is a connected topological space that has a homotopy type of a CW complex and whose fundamental group is abelian and acts trivially on the homotopy and homology of the universal covering space, though not all authors include the assumption on the homotopy type.
For example, any topological group is a simple space (provided it satisfies the condition on the homotopy type).
are simple since the only nontrivial homotopy group is in degree
This means the only non-simple spaces are
Every connected topological space
This topology-related article is a stub.