In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, the corona or corona set of a
topological space ''X'' is the
complement β''X''\''X'' of the space in its
Stone–Čech compactification β''X''.
A topological space is said to be
σ-compact if it is the union of
countably many
compact subspaces, and
locally compact In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space. More precisely, it is a topological space in which ev ...
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
*{{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, doi-access=free
Topology