A characterization of boolean spaces

A characterization of boolean spaces

A boolean space is a compact Hausdorff space which is zero-dimensional. In this paper, a boolean space X is characterized in terms of its ring of real-valued functions C(X). The result is sharpened for the case when X is an F-space (every finitely generated ideal of C(X) is principal).

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 1975-02, Vol.12 (1), p.89-93
Hauptverfasser: Dickerson, C.E., Moore, M.E.
Format: Artikel
Sprache:eng
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Zusammenfassung:A boolean space is a compact Hausdorff space which is zero-dimensional. In this paper, a boolean space X is characterized in terms of its ring of real-valued functions C(X). The result is sharpened for the case when X is an F-space (every finitely generated ideal of C(X) is principal).
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700023662