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
Closure operator
An exercise on topologies from interior operators
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
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
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
Formalis Mathematica 