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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.29 n.3 Antofagasta dic. 2010

http://dx.doi.org/10.4067/S0716-09172010000300008 

Proyecciones Journal of Mathematics
Vol. 29, N° 3, pp. 291-307, December 2010.
Universidad Católica del Norte
Antofagasta - Chile


FINITE TOPOLOGIES AND DIGRAPHS


Carlos Marijuán


Universidad de Valladolid, España



Correspondencia a:


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.

AMS Classification : 54A05, 05C20.

Keywords : Finite topologies, digraphs.



References

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[3] Evans, J., Harary, F., Lynn, M., On the computer enumeration of finite topologies, Comm. ACM., 10, pp. 295-298, (1967).        [ Links ]

[4] Erné, M., Stege, K., Counting finite posets and topologies topologies, Order, 8, pp. 247-265, (1991).        [ Links ]

[5] Grothendieck, A., Dieudonn´e, J.A., El´ementes de G´eometrie Alg´ebrique I, Springer-Verlag, Berlin, (1971).        [ Links ]

[6] Marijuán, C., Una teor´ia birracional para los grafos ac´iclicos, Ph. D. Dissertation, Universidad de Valladolid, (1988).

[7] Sloane, N. J. A., The on-line encyclopedia of integer sequences published electronically.        [ Links ]

[8] Willard, S., General topology, Addison-Wesley, (1970)        [ Links ]

C. Marijuán
Dpto. Matemática Aplicada
E.T.S.I. Informática
Paseo de Bel´en 15
47011-Valladolid
Spain
e-mail : marijuan@mat.uva.es


Received : October 2010. Accepted : November 2010

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