Rickart space

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. Grove & Pedersen (1984) named them after C. E. Rickart (1946), 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 spaces.

References

• Grove, Karsten; Pedersen, Gert Kjærgård (1984), "Sub-Stonean spaces and corona sets", Journal of Functional Analysis 56 (1): 124–143, doi:10.1016/0022-1236(84)90028-4, ISSN 0022-1236, MR 735707 
• Rickart, C. E. (1946), "Banach algebras with an adjoint operation", Annals of Mathematics. Second Series 47: 528–550, ISSN 0003-486X, JSTOR 1969091, MR 0017474