Some Properties Of Generalized Topological Space Research

The notion of generalized topology was introduced by A. Csaszar, a Hungarian mathe-matician, in 2002. Now the basic framework has already been established, which has attracted wide attention of many international researchers.In this paper, we introduce, on the basis of A. Csasza' s studying, the notions of g-irresolute function, g-connectedness, g-local compactness, g-quotient topology and so on. We investigate properties of g-irresolute functions, the equivalent properties of the g-connected component, the local g-connectedness and prove the Pasting Lemma and the Ti(g) (i=1,2) spaces, the reg-ular generalized space and normal generalized space are strong generalized topological spaces. Furthermore we mainly focus on the hereditary property and the productive property of these separation spaces in generalized topological spaces. We also focus on local compactness in gen-eralized topological spaces, and obtain some properties and characterizations. Local g-compact generalized topological space is strong. Every g-closed subspace of a local g-compact space is local g-compact. A product of finite local g-compact spaces is local g-compact. In the end, we study the g-quotient topology, g-quotient mapping, and obtain some properties and characteri-zations of them.