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It is well-known that Galois connections are useful in describing some situations that occur naturally in computer science and mathematics; and recently it has been shown that Lagois connections, which are closely related to Galois connections, are similarly useful. Thus, it is natural to ask if there are not common generalizations of Galois and Lagois connections which would be useful in both disciplines...
A notion of separation with respect to an interior operator in topology is introduced and some basic properties are presented. In particular, it is shown that this notion of separation with respect to an interior operator gives rise to a Galois connection between the collection of all subclasses of the class of topological spaces and the collection of all interior operators in topology. Characterizations...
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