Research On Strong Semi-regular Maximal Spaces And LF Almost Strong F-compactness

In this paper, our major concern is to introduce a new definition called strong semi-regular space and also some equivalent conditions of the first countable T2 strong semi-regular maximal spaces within the range of general topology are studied. In addition, the concept of almost compactness space in general topology and its important properties are generlized to L -fuzzy topological spaces .The primary studies are the following:1. In general topology, we give a new definition called strong semi-regular space and also some equivalent conditions of the first countable T2 strong semi-regular maximal space are studied. at last, it is proved that if X is the first countable T2 strong semi-regular spaces,then the following conditions are equivalent.(1) X is the first countable T2 strong semi--regular maximal spaces;(2) X is the first countable T2 strong semi-regular minimal spaces;(3) X is the first countable T2 strong semi-regular closed spaces;(4) Every countable open filter base which has an only accumulation point in X is convergent to the accumulation point;(5) X is the first countable T2 feebly compactness strong sime-regular spaces .2. In L -fuzzy topological spaces, we introduce the concepts ofθ-convergence for anα?net and almost strong F - compactness. and give various characterizations of almost strong F - compactness, we prove almost strong F - compactness possesses the properties such as finite sum, can be preserved under continious full L -zadeh functions and so on,is a L -good extension of almost compactness. Finally, some important results of compactness are generlized to L -fuzzy topological spaces .