Carrillo Blanquicett, Alexis

Publication Search Results

Now showing 1 - 1 of 1

Coseparation with respect to an interior operator in topology
(2018-05) Carrillo Blanquicett, Alexis; Castellini, Gabriele; College of Arts and Sciences - Sciences; Ortiz, Juan A.; Romero, Juan; Rivera Marrero, Olgamary; Department of Mathematics; Rios, Isabel
Motivated by the results obtained in the paper [1], concerning the notion of separation for an interior operator in topology, the notion of I-coseparation for an interior operator I in topology is introduced. A few examples that illustrate the behavior of this notion are presented for concrete interior operators in topology. Subsequently, it is determined under which topological properties this notion is closed. Later, it is obtained that in particular the I-coseparated topological spaces are closed under direct images of continuous functions and under quotient spaces but they are not closed under topological sums and topological subspaces. It is proved that the notion of I-coseparation generates a Galois connection between the class of all interior operators in topology and the conglomerate of all the subclasses of topological spaces. Using this result, a commutative diagram of Galois connections that shows the relationship between the notions of I-separation and I-coseparation is presented. Finally, it is proved that a characterization of the I-coseparated spaces in terms of separators, analogous to the one presented in [1] for the notion of I-separation, is not possible.