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 of a set
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 