On partitioning the triples of a topological space
The authors prove the following result. Proposition A: The existence of a 0-dimensional \(T_ 2\)-space \(X\) of cardinality \(\aleph_ 3\) such that every partition of triples of \(X\) into countably many pieces has a nondiscrete homogeneous set. Proposition A is consistent with GCH. An open problem is stated: Does GCH imply Proposition A? Moreover, does ZFC imply Proposition A (in this case \(X\) is \(T_ 3\)-space)?
scientific article; zbMATH DE number 123576
scientific article