An operator on a set S, i.e. an extensive and monotone (but not necessarily idempotent) function on the power set of S, generalizes the familiar notion of closure operator (transitive operator). This is one of several equivalent ways to define a dependence system. In this paper a brief review of dependence system theory precedes a more detailed discussion of some particular properties, e.g. the operator-image exchange property. Once again the duality of operators and resulting duality of properties of dependence systems (defined only when nontransitive operators are admitted), makes it possible to relate properties thus far studied in the context of separate mathematical theories.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics