Communications of the
Korean Mathematical Society CKMS

We define a stratification and a partition of a finite topological space and define a partial order on the partition. Open subsets can be described completely in terms of this partially ordered partition. We associate a directed graph to the partially ordered partition of a finite topological space. This gives a one-to-one correspondence between finite topological spaces and a certain class of directed graphs.

Keywords: finite topological space, directed graph, duality

MSC numbers: 54A05, 05C20