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A general separation theorem for various structures. (English) Zbl 07301178

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 Z. Páles [Arch. Math. 52, No. 3, 265–268 (1989; Zbl 0651.20067)].

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
06A15 Galois correspondences, closure operators (in relation to ordered sets)
05B35 Combinatorial aspects of matroids and geometric lattices

Citations:

Zbl 0651.20067
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References:

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