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
Bijection
An exercise on the characteristic function and the Sierpinski-space
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
Nombres entiers naturels puissants consécutifs
Un entier naturel $latex n$ est appelé nombre puissant lorsque, pour tout diviseur premier $latex p$ de $latex n$, le carré $latex p^{2}$ divise $latex n$. Par exemple, étant donné un nombre premier $latex p$ et un entier $latex m\geq 2$, l'entier $latex n=p^{m}$ est un nombre puissant. En effet, $latex p$ est l'unique diviseur … Lire la suite de Nombres entiers naturels puissants consécutifs
Formalis Mathematica 