# zbMATH — the first resource for mathematics

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 $$c(X)\leq 2^{\omega}$$.