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Antichains and finite sets that meet all maximal chains. (English) Zbl 0606.06001
If P is an ordered set, by M(P) is denoted the set of all maximal chains of P. M(P) is regarded as a subspace of \(2^{| P|}\). A cutset for \(x\in P\) is a set C(x)\(\subset P\) all of whose elements are noncomparable to x and each maximal chain of P includes x or some element of C(x). A countably chain complete ordered set with the finite cutset property contains no uncountable antichain. If there is a chain complete ordered set P whose space M(P) is homeomorphic to a compact topological space X then the cellularity c(X) of X satisfies \(c(X)\leq 2^{\omega}\).
Reviewer: D.Adnadjević

MSC:
06A06 Partial orders, general
06B30 Topological lattices
57N60 Cellularity in topological manifolds
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