Finite topologies and digraphs

Authors

  • Carlos Marijuán López Universidad de Valladolid.

DOI:

https://doi.org/10.4067/S0716-09172010000300008

Keywords:

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.

Author Biography

Carlos Marijuán López, Universidad de Valladolid.

Departamento de Matemática Aplicada, ETS de Ingeniería Informática.

References

Alexandroff, P. S., Diskrete Rume, Matematiceskii Sbornik (N.S.) 2, pp. 501-518, (1937).

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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