Parovicenko space
In mathematics, a Parovicenko space is a topological space similar to the space of non-isolated points of the Stone–Čech compactification of the integers.
Definition
A Parovicenko space is a topological space X satisfying the following conditions:- X is compact Hausdorff
- X has no isolated points
- X has weight of a [topological space|weight] c, the cardinality of the continuum.
- Every two disjoint open Fσ subsets of X have disjoint closures
- Every non-empty Gδ of X has non-empty interior.