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On a generalization of approximation space. (English) Zbl 0755.04011
Summary: We consider approximation spaces as ordered triples (U,F,G) composed of a nonempty set U and two set-theoretical operations F, G:P(U)P(U) such that for any XU:F(X)={F({x}):xX} and G(x)={yU:F({y})X}. Operations F, G are in particular, respectively, the upper and lower approximation operations of Z. Pawlak and certain variants of the latter. We establish various properties of F, G and at the same time known and new properties of approximations. In particular, we give necessary and sufficient conditions for F, G to be the topological closure and interior operations in the sense of K. Kuratowski [Fundam. Math. 3, 182-199 (1922; JFM 48.0210.04)], respectively.
03E99Set theory (logic)
54A99Generalities of general topology
03E20Other classical set theory (logic)