On Topologies and Reflexive Transitive Relations On Finite Sets

Severino Docto  Diesto,

On Topologies and Reflexive Transitive Relations On Finite Sets

Abstract:

For finite sets, the concepts of topology and reflexive transitive relations are shown to be equivalent; thus a topologv on a finite set can be represented by an incidence relation, and a function between finite topological spaces has a matrix representation. A theorem on when and only when this matrix representation is a representation for a continuous function is then given.