In mathematics, a Rickart space (after Charles Earl Rickart), also called a basically disconnected space, is a topological space in which open ÃÂ-compact subsets have compact open closures.
named them after , who showed that Rickart spaces are related to monotone ÃÂ-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 ÃÂ-spaces, as they correspond to Boolean ÃÂ-algebras via Stone duality. The concept of Rickart spaces resurfaced in under the name Stone<sub>ÃÂ</sub>-spaces.
Both algebraic descriptions (namely, the C*-algebraic and Boolean algebraic ones) are explicitly discussed in .
Rickart spaces are totally disconnected and sub-Stonean spaces.