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- Title
On Ideal Closure Operators of M-Sets.
- Authors
Ebrahimi, M. Mehdi
- Abstract
Closure operators have been used in Algebra aim Topology. Well-known examples are the closure of a subspace of a topological space, or the normal closure of a subgroup of a group. Category theory provides a variety of notions which expand on the lattice theoretic concept of closure operator which leads to a never ending stream of examples and applications in all areas of mathematics. Actions of a monoid have always been a useful tool to study the mathematical structures, and recently have captured the interest of some computer scientists. For this reason and because of its closed relation to the category of sets, one can take the topos MSet of M-sets, for a monoid M, as the "universe of discourse" to study mathematical notions in it. Here, using the general definition of a closure operator on a category, we introduce and investigate some properties, such as idempotency, additivity, and hereditariness for ideal closure operators of the category of M-sets.
- Subjects
CLOSURE operators; LATTICE theory; GALOIS correspondences; CATEGORIES (Mathematics); GROUP theory
- Publication
Southeast Asian Bulletin of Mathematics, 2006, Vol 30, Issue 3, p439
- ISSN
0129-2021
- Publication type
Article