Math 223 B Winter 2005
نویسنده
چکیده
(a) P is a nonempty set; (b) ≤ is a partial ordering of P; i.e., ≤ is transitive, reflexive relation in P (and so p ≤ q ∧ q ≤ p ∧ p 6= q is not forbidden); (c) for all p ∈ P, p ≤ 1. (1 need not be the only such maximum element.) We shall often write P for 〈P,≤,1〉. Let P be a poset. If p is an element of P, then an extension of p is a q ∈ P such that q ≤ p. Two elements of P are compatible if they have a common extension. We write p ⊥ q to mean that p and q are incompatible. A subset D of P is dense in P if every element of P has an extension that belongs to D. A filter on a poset P is a non-empty subset F of P satisfying:
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تاریخ انتشار 2005