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==References== |
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*{{Citation | last1=Grove | first1=Karsten | last2=Pedersen | first2=Gert Kjærgård | title=Sub-Stonean spaces and corona sets | doi=10.1016/0022-1236(84)90028-4 | mr=735707 | year=1984 | journal=Journal of Functional Analysis | issn=0022-1236 | volume=56 | issue=1 | pages=124–143}} |
*{{Citation | last1=Grove | first1=Karsten | last2=Pedersen | first2=Gert Kjærgård | title=Sub-Stonean spaces and corona sets | doi=10.1016/0022-1236(84)90028-4 | mr=735707 | year=1984 | journal=[[Journal of Functional Analysis]] | issn=0022-1236 | volume=56 | issue=1 | pages=124–143}} |
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[[Category:Topology]] |
[[Category:Topology]] |
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Revision as of 20:28, 14 June 2021
In mathematics, the corona or corona set of a topological space X 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 corona 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