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 … Lire la suite de The right topology, the left topology and Kolmogoroff spaces
Mathematics
Properties of the frontier operator
The framework of this publication is an exercise of the volume on General Topology by Bourbaki (cf. Exercise 5 of the section §1 in Chapter I). The paper, divided into five sections, is devoted to the frontier operator and some of its properties. The first section gives the definition of the frontier and some elementary … Lire la suite de Properties of the frontier operator
All topologies on a set with two or three elements
A topology on a set X is a set O of subsets of X satisfying the following two conditions: firstly, every union of sets of O is a member of O; secondly, every finite intersection of sets of O belongs to O. A topology on X is thus a subset of the power set of … Lire la suite de All topologies on a set with two or three elements
Formalis Mathematica 