Local T_0 semi uniform limit convergence spaces

The category SULim of semi uniform limit convergence spaces (and unifomly continuous maps) is a strong topological universe, i.e., a cartesian closed and hereditary topological category. Moreover, in topological category SULim, products of quotients are quotients. The aim of this paper is to characterize local T_0 semi uniform limit convergence spaces at a point p. This thesis is divided into six chapters. A brief description of the contents of each follows: In the first chapter, the history of semi uniform limit convergence spaces is emphasized and it is a literature review. In the second chapter, some basic definitions such as the category, functor, natural transformation and topological functor which will be needed later are given. In the third chapter, basic definitions, properties related to filter and uniform space concepts and some results that we will use in the fifth chapter are given. In the fourth chapter, the category of semi uniform limit convergence spaces SULim has been shown to be the topological category. Later, some special objects and morphisms in this category are characterized. In the fifth chapter, in the category SULim, T0 semi uniform limit convergence space at a point p is characterized. Finally, the category T ̅0SULim is created and some important results are given. In the last chapter, results and recommendations were given.