// Workers AI · dad joke modeWhat did the Stone–Čech remainder say? "I'm left over.

In mathematics, the Stone–Čech remainder of a topological space X, also called the corona or corona set, is the complement βX \ X of the space in its Stone–Čech compactification βX.

A topological space is said to be σ-compact if it is the union of countably many compact subspaces, and locally compact if every point has a neighbourhood with compact closure. The Stone–Čech remainder of a σ-compact and locally compact Hausdorff space is a sub-Stonean space, i.e., any two open σ-compact disjoint subsets have disjoint compact closures.

See also

• Corona theorem
• Corona algebra, a non-commutative analogue of the corona set.

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 0735707