The paper is devoted to the study of the ordered set AK(X,a) of the (equivalence classes of) A-compactifications of an Alexandroff space (X,a). The notion of A-weight of an Alexandroff space is introduced and investigated. Lattice properties of AK(X,a) and of the subfamily AK_w(X,a), consisting of the A-compactifications of (X,a) having the same A-weight of (X,a), are studied. A characterization of families of the continuous bounded real functions on X which generate an A-compactification of (X,a) is obtained. A-determining families of functions are defined and studied. In particular a characterization of the families of continuous bounded real functions which A-determine a given A-compactification is established and the minimum cardinality of an A-determining family is studied.

A-compactifications and A-weight of Alexandroff spaces

CATERINO, Alessandro;VIPERA, Maria Cristina
2002

Abstract

The paper is devoted to the study of the ordered set AK(X,a) of the (equivalence classes of) A-compactifications of an Alexandroff space (X,a). The notion of A-weight of an Alexandroff space is introduced and investigated. Lattice properties of AK(X,a) and of the subfamily AK_w(X,a), consisting of the A-compactifications of (X,a) having the same A-weight of (X,a), are studied. A characterization of families of the continuous bounded real functions on X which generate an A-compactification of (X,a) is obtained. A-determining families of functions are defined and studied. In particular a characterization of the families of continuous bounded real functions which A-determine a given A-compactification is established and the minimum cardinality of an A-determining family is studied.
2002
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/152442
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