# Applications of Finite Topologies with Maple Software.

## Institution

Murray State University

## Faculty Advisor/ Mentor

John Porter

## Abstract

A topology T on set X is a family of subsets of X that satisfies the following conditions: i) T is closed under arbitrary unions, ii) T is closed under finite intersections, iii) and X and the empty set are in X. Let T(n) denote the number of topologies on a finite set with n elements. The relationship of finite topologies to Boolean matrices, Boolean functions, and lattices is investigated with the use of Maple Software. Boolean functions, Boolean matrices, and lattice shave many applications to computer science such as network design, decision theory, and coding theory. The relationship with these concepts and the seemingly unrelated topic of finite topologies is investigated with the use of Maple software.

Applications of Finite Topologies with Maple Software.

A topology T on set X is a family of subsets of X that satisfies the following conditions: i) T is closed under arbitrary unions, ii) T is closed under finite intersections, iii) and X and the empty set are in X. Let T(n) denote the number of topologies on a finite set with n elements. The relationship of finite topologies to Boolean matrices, Boolean functions, and lattices is investigated with the use of Maple Software. Boolean functions, Boolean matrices, and lattice shave many applications to computer science such as network design, decision theory, and coding theory. The relationship with these concepts and the seemingly unrelated topic of finite topologies is investigated with the use of Maple software.