Topological space with trivial cup product

Definition
A topological space is said to have 'trivial cup product if for $$i,j > 0$$, the cup product between the $$i^{th}$$ and $$j^{th}$$ cohomology groups is trivial.

Stronger properties

 * Acyclic space
 * Sphere
 * Suspension space

Metaproperties
A wedge sum of topological spaces, each with trivial cup product, continues to have trivial cup product.