Coreflective hull of finite strong L-topological spaces
The authors prove that for each unital quantale \(L\), the category of Alexandroff strong \(L\)-co-topological spaces is the coreflective hull of finite strong \(L\)-co-topological spaces. On the other hand, in the case that the quantale \(L\) is the unit interval \([0,1]\) equipped with a continuous t-norm, they prove that the category of Alexandroff strong \([0,1]\)-topological spaces is the coreflective hull of finite strong \([0,1]\)-topological spaces if and only if the continuous t-norm is an ordinal sum of the Łukasiewicz t-norm whose set of idempotent elements is a well-ordered subset of \([0,1]\) under the usual order.
scientific article; zbMATH DE number 6048006