In mathematics, a Rickart space (after Charles Earl Rickart), 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.See Section 22, specifically Theorem 12, in . The concept of Rickart spaces resurfaced in under the name Stoneσ-spaces.
Both algebraic descriptions (namely, the C*-algebraic and Boolean algebraic ones) are explicitly discussed in .See Corollary 2.1.17 and Fact 3.1.10.
Rickart spaces are totally disconnected and sub-Stonean spaces.
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