Finite topologies and digraphs
DOI:
https://doi.org/10.4067/S0716-09172010000300008Keywords:
Finite topologies, digraphs, topologías finitas, digrafos.Abstract
In this paper we study the relation between finite topologies and digraphs. We associate a digraph to a topology by means of the “specialization” relation between points in the topology. Reciprocally, we associate a topology to each digraph, taking the sets of vertices adjacent (in the digraph) to v, for all vertex v, as a subbasis of closed sets for the topology. We use these associations to examine the relation between a simple digraph and its homologous topology. We also extend this relation to the functions preserving the structure between these classes of objects.References
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Benoumhani, M., The number of topologies on a finite set, J. of Integer Sequences, Vol. 9, Article 06.2.6, (2006).
Evans, J., Harary, F., Lynn, M., On the computer enumeration of finite topologies, Comm. ACM., 10, pp. 295-298, (1967).
Erné, M., Stege, K., Counting finite posets and topologies topologies, Order, 8, pp. 247-265, (1991).
Grothendieck, A., Dieudonné, J.A., Elémentes de Géometrie Algébrique I, Springer-Verlag, Berlin, (1971).
Marijuán, C., Una teoría birracional para los grafos acíclicos, Ph. D. Dissertation, Universidad de Valladolid, (1988).
Sloane, N. J. A., The on-line encyclopedia of integer sequences published electronically.
Willard, S., General topology, Addison-Wesley, (1970).
Published
2011-01-07
How to Cite
[1]
C. Marijuán López, “Finite topologies and digraphs”, Proyecciones (Antofagasta, On line), vol. 29, no. 3, pp. 291-307, Jan. 2011.
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