Algebraic Topological Closure Operators

Autor: R. Seshagiri Rao, U. M. Swamy
Rok vydání: 2003
Předmět:
Zdroj: Southeast Asian Bulletin of Mathematics. 26:669-678
ISSN: 0219-175X
0129-2021
DOI: 10.1007/s100120200071
Popis: For any closure operator c there is a To-closure operator whose lattice of closed subsets are isomorphic to that of c. A correspondence between algebraic topological (To) closure operators on a nonempty set X and pre-orderes (partial orders) on X is established. Equivalent conditions are obtained for a To-lattice to be a complete atomic Boolean algebra and for the lattice of closed subsets of an algebraic topological closure operator to be a complete atomic Boolean algebra. Further it is proved that a complete lattice is an algebraic To-lattice if and only if it is isomorphic to the lattice of closed subsets of some algebraic topological closure operator on a suitable set.
Databáze: OpenAIRE
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