Show simple item record

dc.contributor.advisorCastellini, Gabriele
dc.contributor.authorCortez-Portillo, Henrry J.
dc.description.abstractA 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.en_US
dc.description.abstractUna noción general de separación T1 con respecto a un operador de interior arbitrario es presentada en la categoría Top de los espacios topológicos. Esto es hecho por medio del concepto de operador de interior categórico. Esto naturalmente implica una noción dual de coseparación T1. Cada una de estas dos nociones produce una conexión de Galois entre los operadores de interior categóricos en Top y las subclases de espacios topológicos. Estas dos conexiones de Galois son estudiadas y es mostrado que su composición puede ser descrita como una conexión de Galois definida en términos del concepto de función constante. Esto puede fácilmente ser mostrado con un diagrama conmutativo de conexiones de Galois.en_US
dc.subjectTopological spacesen_US
dc.subjectGalois modules (Algebra)en_US
dc.subjectClosure operatorsen_US
dc.subject.lcshTopological spacesen_US
dc.subject.lcshGalois theoryen_US
dc.titleInterior operators and T1 topological spacesen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c) 2018 Henrry Josue Cortez-Portilloen_US
dc.contributor.committeeOrtiz-Albino, Reyes M.
dc.contributor.committeeOrtiz-Navarro, Juan A.
dc.contributor.committeeRivera-Marrero, Olgamary
dc.contributor.representativeCruz-Martínez, Darik Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences - Sciencesen_US
dc.contributor.departmentDepartment of Mathematicsen_US

Files in this item


This item appears in the following Collection(s)

  • Theses & Dissertations
    Items included under this collection are theses, dissertations, and project reports submitted as a requirement for completing a graduate degree at UPR-Mayagüez.

Show simple item record

All rights reserved
Except where otherwise noted, this item's license is described as All Rights Reserved