On the enumeration of homeomorphism classes of finite topologies

Abstract

AbstractAn algorithm called UNLABEL is devised to uniquely label an unlabelled transitive digraph. This is used to construct a one-one correspondence between homeomorphism classes of finite nondiscrete To-topologies and certain generalised Young tableaux of shape-type α. For sets of cardinality 2, 3, 4 and 5 these classes are enumerated and classified in several ways. The notion of a generalised descriptor graph is then introduced to enumerate the homeomorphism classes of all topologies on these sets.