FINITE TOPOLOGIES AND DIGRAPHS

FINITE TOPOLOGIES AND DIGRAPHS

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 (...

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Autor principal: Marijuán,Carlos
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2010
Materias:
Finite topologies
digraphs
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000300008
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spelling oai:scielo:S0716-091720100003000082010-12-29FINITE TOPOLOGIES AND DIGRAPHSMarijuán,Carlos Finite topologies digraphs 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.29 n.3 20102010-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000300008en10.4067/S0716-09172010000300008
institution Scielo Chile
collection Scielo Chile
language English
topic Finite topologies
digraphs
spellingShingle Finite topologies
digraphs
Marijuán,Carlos
FINITE TOPOLOGIES AND DIGRAPHS
description 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 Marijuán,Carlos
author_facet Marijuán,Carlos
author_sort Marijuán,Carlos
title FINITE TOPOLOGIES AND DIGRAPHS
title_short FINITE TOPOLOGIES AND DIGRAPHS
title_full FINITE TOPOLOGIES AND DIGRAPHS
title_fullStr FINITE TOPOLOGIES AND DIGRAPHS
title_full_unstemmed FINITE TOPOLOGIES AND DIGRAPHS
title_sort finite topologies and digraphs
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2010
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000300008
work_keys_str_mv AT marijuancarlos finitetopologiesanddigraphs
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