Finite topological spaces and graphs
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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.
Abstract
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.
참고문헌 (3)
- J. Gross, "Graph Theory and its Applications", pp.2006, Chapman and Hall
- M. Mariju´an, "Finite Topologies and Digraphs", Proyecciones, 29(3), pp.291~307 (2010)
- J. Munkres, "Topology" (2000), Pearson