Topologies on a set can be defined by the means of neighborhood systems. In this note, we prove that topologies can also be constructed using closure operators. In fact, the note is a solution of an exercise formulated in a previous entry of this blog. We repeat the statement of the exercise in question here, … Lire la suite de Topologies from closure operators
Closed set
An exercise on topologies from closure operators
It is well-known that a topology on a set can be defined by the means of a neighborhood system. Topologies can also arise from certain operators. In this note, we set an exercise, which invites to prove that topologies can be obtained from closure operators. The exercise statement below provides a clear definition of closure … Lire la suite de An exercise on topologies from closure operators
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
Formalis Mathematica 