UNCOUNTABLE FAMILIES OF PRIME z-IDEALS IN C0(R)
نویسنده
چکیده
Denote by c = 2א0 the cardinal of continuum. We construct an intriguing family (Pα : α ∈ c) of prime z-ideals in C0(R) with the following properties: • If f ∈ Pi0 for some i0 ∈ c, then f ∈ Pi for all but finitely many i ∈ c; • T i6=i0 Pi 6⊂ Pi0 for each ı0 ∈ c. We also construct a well-ordered increasing chain, as well as a well-ordered decreasing chain, of order type κ of prime z-ideals in C0(R) for any ordinal κ of cardinality c.
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تاریخ انتشار 2008