Murcia-Rodríguez, Edwin G.

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The notion of separation for interior operators in topology
(2010-12) Murcia-Rodríguez, Edwin G.; Castellini, Gabriele; College of Arts and Sciences - Sciences; Barety, Julio E.; Cáceres Duque, Luis F.; Department of Mathematics; Seguel, Jaime
A notion of separation with respect to an interior operator in topology is introduced. After concrete examples, some properties of separation are presented. In particular, closure of separation with respect to subspaces and products is proved. This notion of separation with respect to an interior operator gives rise to a Galois connection between the collection of all Topological Spaces and the collection of all Interior Operators in Topology. Characterizations of the fixed points of this Galois connection are given. An equivalent definition of separation is introduced that makes possible a generalization to other categories as well. Examples are provided.