The author starts from a binary relation on a set and then defines a so-called modifier by:
When the relation is reflexive, i.e. is called an accessibility relation, then is called a weakening modifier. To every weakening modifier a so-called substantiating modifier is defined by . The main results concern the interaction between set-theoretic union, intersection, inclusion on the one hand and weakening and substantiating modifiers on the other hand. The proofs are very simple. Finally it is shown that certain modifiers are topological closure operators and that rough sets can be obtained as modifiers.
This paper can be described as old wine in new bottles. Indeed is nothing but the direct image of under the binary relation and is easily identified as the superdirect image of under a reflexive relation . Hence all the main results were well known.