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Symmetrization of Closure Operators and Visibility

✍ Scribed by Horst Martini; Walter Wenzel

Publisher
Springer
Year
2005
Tongue
English
Weight
200 KB
Volume
9
Category
Article
ISSN
0218-0006

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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.

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A general notion of connectedness with respect to a closure operator on an arbitrary category X is used to produce some connectedness notions in the category of fuzzy topological spaces. All these notions turn out to be connectednesses in the sense of PreuB. Some already existing notions of connecte