Auteur : Christian Nguembou Tagne

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Ouvrage d’arithmétique : Guide complet pour enseignants et apprenants

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La géométrie et l'arithmétique sont les toutes premières disciplines mathématiques pratiquées par l'homme. Elles constituaient alors une boîte à outils pour résoudre les problèmes du quotidien. Dans le monde contemporain, l'arithmétique est étudiée à tous les niveaux d'enseignement. Nous avons travaillé sur les thèmes d'arithmétique inscrits dans les programmes de l'enseignement secondaire, notamment dans les … Lire la suite de Ouvrage d’arithmétique : Guide complet pour enseignants et apprenants

A characterization of the existence of an interior point

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We recall that, in a topological space, a point is said to be an interior point of a subset if the latter is a neighborhood of the point in question. The set of interior points of a subset is called the interior of this subset. It is well-known that a subset is open if and … Lire la suite de A characterization of the existence of an interior point

An exercise on a characterization of the existence of an interior point

/ Christian Nguembou Tagne / 1 commentaire

We recall that, in a topological space, a point is said to be an interior point of a subset if the latter is a neighborhood of the point in question. The set of interior points of a subset is called the interior of this subset. It is well-known that a subset is open if and … Lire la suite de An exercise on a characterization of the existence of an interior point

Topologies from interior operators

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As seen in a preceding entry of this blog, topologies on a set can be defined by the means of closure operators. In this note, we prove that topologies can also be constructed using interior operators. In fact, the note is a solution of an exercise formulated previously. We repeat the statement of the exercise … Lire la suite de Topologies from interior operators

An exercise on topologies from interior operators

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In a preceding entry of this blog, we saw that topologies arise from closure operators. This note raises the question of whether this is also valid for interior operators. The question is framed precisely in the exercise below. To approach the issue with serenity, it should be remembered here that closure and interior are dual … Lire la suite de An exercise on topologies from interior operators

Topologies from closure operators

/ Christian Nguembou Tagne / 2 Commentaires

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

An exercise on topologies from closure operators

/ Christian Nguembou Tagne / 1 commentaire

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

The characteristic function and the Sierpinski-space

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A topological space, whose underlying set has two elements, is called the Sierpinski-space if its topology is non-discrete and non-indiscrete. In this publication, we give a necessary and sufficient condition for the continuity of a characteristic function from a topological space into the Sierpinski-space. In fact, this is our solution to an exercise outlined in … Lire la suite de The characteristic function and the Sierpinski-space

An exercise on the characteristic function and the Sierpinski-space

/ Christian Nguembou Tagne / 1 commentaire

The characteristic function appears in many fields of mathematics. This publication set an exercise that allows to discover elementary features of the characteristic function in the context of Set Theory and General Topology. The exercise also introduces the Sierpinski-space. In a preceding entry of this blog, we established that there exactly four topologies on a … Lire la suite de An exercise on the characteristic function and the Sierpinski-space

Applications linéaires d’une somme directe d’espaces vectoriels dans un produit d’espaces vectoriels

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Nous introduisons dans cette contribution l'isomorphisme canonique, de l'espace vectoriel des applications linéaires d'une somme directe dans un produit, sur un produit d'espaces vectoriels d'applications linéaires. Nous examinerons également quelques cas particuliers de cet isomorphisme. Il s'agit en réalité d'une solution à un exercice proposé dans un article précédent. Dans l'argumentation, nous faisons usage de … Lire la suite de Applications linéaires d’une somme directe d’espaces vectoriels dans un produit d’espaces vectoriels