Cortez-Portillo, Henrry J.

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Interior operators and T1 topological spaces
(2018-05) Cortez-Portillo, Henrry J.; Castellini, Gabriele; College of Arts and Sciences - Sciences; Ortiz-Albino, Reyes M.; Ortiz-Navarro, Juan A.; Rivera-Marrero, Olgamary; Department of Mathematics; Cruz-Martínez, Darik
A general notion of T1-separation with respect to an arbitrary interior operator is introduced in the category Top of topological spaces. This is done by means of the concept of categorical interior operator. This naturally yields a dual notion of T1-coseparation. Each of these two notions produces a Galois connection between categorical interior operators in Top and subclasses of topological spaces. These two Galois connections are studied and it is shown that their composition can be described as a classical Galois connection de ned in terms of the concept of constant function. This can be easily illustrated with a commutative diagram of Galois connections.