Description:
Definitions from Bell [1988]
Content:
Definitions from Bell [1988]
Definition: Assume that \(X\) and \(Y\) are topological
spaces.
- If \(f\) is a continuous surjection from \(X\) onto \(Y\), \(f\) is
irreducible if the image of a proper closed subset of \(X\) is a
proper subset of \(Y\).
- \(X\) is 0-dimensional if \(X\) has a base of clopen sets.
- \(X\) is Boolean if \(X\) is compact, Hausdorff and
0-dimensional.
- \(X\) is extremally disconnected if the closure of any
open set is open.
- \(X\) is \(\sigma\)-extremally disconnected if \(X\) is
0-dimensional and the algebra of clopen subsets of \(X\) is
\(\sigma\)-complete (that is, countably complete). (From Morillon [1993]
- If \(X\) is compact Hausdorff, a Gleason cover of \(X\) is a pair \((E,\pi)\) where \(E\) is an extremally disconnected compact Hausdorff space and \(\pi\) is an irreducible continuous surjection \(\pi : E \to X\).
Howard-Rubin number:
114
Type:
Definitions
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