Closure operators on a lattice
✍ Scribed by S. L. Édel'man
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1981
- Tongue
- English
- Weight
- 673 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0037-4466
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The system of all the closure operators on a set V forms a lattice. This lattice is isomorphic to the lattice of all the Moore families of subsets of V. This paper describes basic properties of these lattices, and gives a method to find all the members of these lattices.
## Abstract A theorem of Birkhoff‐Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many‐sorted sets, i.e., indexed families of sets, such a theorem is not longer