Closure operators are abundant in mathematics; here are a few examples. Given an algebraic structure, such as group, ring, field, lattice, vector space, etc., taking the substructure generated by a set, i.e., the least substructure which includes that set, is a closure operator. Given a binary relation, taking the relation with certain properties, such as reflexive, transitive, equivalence, etc...

We define a closure operation for ideals in a commutative ring which has all the good properties of solid closure (at least in the case of equal characteristic) but such that also every ideal in a regular ring is closed. This gives in particular a kind of tight closure theory in characteristic zero without referring to positive characteristic.

We consider rings equipped with a closure operation defined in terms of a collection of commuting idempotents, generalising the idea of a topological closure operation defined on a ring of sets. We establish the basic properties of such rings, consider examples and construction methods, and then concentrate on rings which have a closure operation defined in terms of their lattice of central ide...

Starting from the observation that rational closure has the undesirable property of being an “all or nothing” mechanism, we here propose a multipreferential semantics, which enriches the preferential semantics underlying rational closure in order to separately deal with the inheritance of different properties in an ontology with exceptions. We provide a multipreference closure mechanism which i...

the main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by özkoç and aslım cite{10} called weakly $er$-open functions and $e$-$theta$-open functions. moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing to...

The paper describes a preferential approach for dealing with exceptions in KLM logics, based on the rational closure. It is well known that closure does not allow an independent handling of inheritance different defeasible properties concepts. In this work, we consider alternative construction, called Multi Preference (MP-closure), which has been first considered reasoning DLs. We reconstruct n...