A subset of a topological space is reducible if it can be written as a union of two closed proper subsets , of (closed in the subspace topology). That is, is reducible if it can be written as a union where , are closed subsets of , neither of which contains .
A subset of a topological space is irreducible (or hyperconnected) if it is not reducible.
As an example, consider with the subspace topology from . This space is a union of two lines and , which are proper closed subsets. So this space is reducible, and thus not irreducible.
|Date of creation||2013-03-22 12:03:30|
|Last modified on||2013-03-22 12:03:30|
|Last modified by||mathcam (2727)|