GEÇİŞLİ DÜZGÜNÜMSÜ UZAYLARIN TEORİSİ

Abstract

In this thesis, a detailed compilation study about the theory of transitive quasi-uniform spaces constructed in peculiar to asymmetric topology as well as the various results, together with the fundamental properties of transitive topological spaces developed within this theory, was presented. The thesis consists of five sections. In the second section of the thesis which starts with Introductionsection, the basic knowledge containing some concepts and results required inside the thesisis mentioned in the context of the theories of topology and uniformity. Following that, quasi-uniform and quasi-proximity spaces known as asymmetric structures in the literature, are mentioned in detail, in the third section consisting of three subsections. Here, some various connections between the structures of quasi-uniform and quasi-proximity, and topological –bitopologica lspaces have been investigated, besides there lationships among these structures. In the fourth section comprising the main topic of thesis, the theory of transitive quasi-uniform structures is handled in two subsections as the transitivequasi-uniform spaces and the transitive topological spaces. According to that, some important characterizations, examples and fundamental results effecting in improving this theory are presented here, widely. The fourth section is concluded by proving that the fact every metrizable space is transitive, and with an associated example. In the last part which is the fifth section, some major results which are obtained in that theory are mentioned, briefly and the thesis finished with the references list.