A general separation theorem for various structures (Q2221011)

In this paper the authors give a general treatment, in ZFC, of separation results with several examples in old and new settings. They define the notion of a solid operator that leads to the notion of separation and also characterize those topological spaces for which the closure of a set is a solid operator. Further, it is proved a separation theorem for solid operators which will be used to characterize those graphic matroids whose span is a solid operator. Also, the separation theorem is used to prove a theorem of \textit{Z. Páles} [Arch. Math. 52, No. 3, 265--268 (1989; Zbl 0651.20067)].