In mathematics, a Rickart space (after Charles Earl Rickart), also called a basically disconnected space, is a topological space

Topological space

Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...

 in which open σ-compact subsets have compact

Compact space

In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, which has many important implications not valid in general spaces...

 open closures. named them after , who showed that Rickart spaces are related to monotone σ-complete C*-algebras in the same way that Stonean spaces are related to AW*-algebras.

Rickart spaces are totally disconnected and sub-Stonean space

Sub-Stonean space

In topology, a sub-Stonean space is a locally compact Hausdorff space such that any two open σ-compact disjoint subsets have disjoint compact closures. They were introduced by...

s.