Approximation operations in approximation space. (English) Zbl 0642.54002

Pomykała, Janusz Andrzej

Bull. Pol. Acad. Sci., Math. 35, No. 1-10, 653-662 (1987).

An approximation space (U,E) is a set U together with a covering \(E=\{E_ t: t\in I\}\). If \(X\subset U\), \(\underline{E}(X)=U\{E_ t: E_ t\subset X\}\) and \(\bar E(X)=U\{E_ t: E_ t\cap X\neq \emptyset \}\). The author discusses when \(\bar E\) is a Kuratowski closure operator and when \(\underline{E}\) is an interior operator. The paper is very interesting.

Reviewer: T.Soundararajan

MSC:

54A05

Topological spaces and generalizations (closure spaces, etc.)

Keywords:

generalized approximation space; closure operator; interior operator