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
Closure
The Kuratowski Closure-Complement Problem
The main goal of this paper, divided into two sections, is to prove a theorem introduced in 1922 by the polish mathematician Kazimierz Kuratowski. This goal shall be accomplished in the second section of the paper with an argumentation, whose algebraic background has been prior exposed in the first section. The Kuratowski Closure-Complement Theorem asserts … Lire la suite de The Kuratowski Closure-Complement Problem
An exercise inspired by the Kuratowski’s Closure-Complement Theorem
In general topology, the Closure-Complement Problem is set as follows: From a given subset A of a topological space and counting A itself, how many sets can be constructed by applying complementation and closure successively? The polish mathematician Kazimierz Kuratowski answered this question in a paper published in 1922. He showed that at most 14 sets … Lire la suite de An exercise inspired by the Kuratowski’s Closure-Complement Theorem
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 