Free Meets in Algebraic Frames
نویسندگان
چکیده
In J. T. Wilson’s doctoral dissertation, the author takes up the subject of free meets, that is, subsets S of a frame L whose meet V S is preserved by a designated class of frame homomorphisms out of L. Wilson proves that all subsets of L have free meets if and only if the dual frame law holds in L and the assembly NL is a boolean frame. In this paper it is shown that for algebraic frames L with the FIP and disjointification, the following are equivalent: (a) L satisfies the dual frame law and Spec(L) the descending chain condition; (b) all subsets of L have free meets; (c) all subsets of L have free meets with respect to all coherent surjective frame maps. If L has these properties, then the assembly is, in fact, atomic.
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