Compacidade generalizada e conceitos relacionados

Abstract

Resumo: Neste trabalho,usamos os conjuntos g-fechados (definidos por N. Levine) e uma variacao destes, os chamados conjuntos ƒÂg-fechados (definidos por Dontchev), para definir tres novas classes de espacos relacionados com a GO-compacidade: Espacos Weakly GOcompactos, Almost GO-compactos e Espacos Nearly GO-compactos. Estudamos muitas de suas propriedades e analisamos a relacao entre eles e entre espacos topologicos ja conhecidos: Espacos GO-compactos, compactos, Nearly-compactos, Almost-compactos e Weakly-compactos. Tambem definimos e investigamos um novo axioma da separacao chamada de almost gregularidade a qual e mais fina que a g-regularidade. Definimos e desenvolvemos a classe dos conjuntos gN-fechados, ƒ¿g-regulares e ƒ¿g-Hausdorff. Tambem desenvolvemos novos resultados relacionados com espacos 4 3 T.

Abstract: By using g-closed sets (as defined by N. Levine) and a variation of those, the so called ägclosed sets (defined by Dontchev) we define three new classes of spaces related to GOcompactness: Weakly GO-compact spaces, Almost GO-compact spaces Nearly GOcompact. We study many of their properties and analyze the relationship between them and between well know topological spaces: O-compact spaces, compact spaces, Nearlycompact spaces, Almost-compact spaces and Weakly-compact spaces. We also define and investigate a new separation axiom called almost g-regularity, which is weaker than the g-regularity. We define and develop gN-closed class, ág-regular and ág- Hausdorff sets. We also obtain new results related to 4 3 T spaces.