Abstract The family T (X) T (X) of all topologies on a given set X, partially ordered by set inclusion, is a complete lattice in which the meet of a collection of topologies is their intersection and the join is the topology with their union as a subbase. In this paper, we first introduce a new partial order on T (X) T (X) and then we investigate some natural questions about the structure of this poset of topologies.
Athanasios Megaritis (Sat,) studied this question.