Rickart space
In mathematics, a Rickart space, also called a basically disconnected space, is a topological space in which open σ-compact subsets have compact open closures.
named them after, who showed that Rickart spaces are related to monotone σ-complete C*-algebras under Gelfand duality, in the same way that Stonean spaces are related to AW*-algebras.
Rickart spaces were also studied by Paul Halmos under the name Boolean σ-spaces, as they correspond to Boolean σ-algebras via Stone duality.
The concept of Rickart spaces resurfaced in under the name Stoneσ-spaces.
Both algebraic descriptions are explicitly discussed in.
Rickart spaces are totally disconnected and sub-Stonean spaces.