Given an ordered set, several topologies can be defined on the underlying set by means of the ordering. In this paper, we introduce two of these topologies: the right topology and the left topology. We also give an introduction to Kolmogoroff spaces. The text is in fact an organized composition on tasks assigned in Exercise 2 of the section §1 in Chapter I of the volume on General Topology by Bourbaki.

The paper is divided into four sections. The first section gives the respective definitions of the right topology and the left topology, as well as some of their features. The second section is devoted to the presentation of the Kolmogoroff spaces. We shall see that the left and right topologies form an important source for Kolmogoroff spaces. In the third section, we show that an ordering can be defined on any Kolmogoroff space, and that the given topology on the Kolmogoroff space is identical with the right topology determined by this ordering, in some cases. The fourth section discuss nature of isolated points in Kolmogoroff spaces. In particular, we will establish a noteworthy consequence of the lack of isolated points in a Kolmogoroff space.