TR available: connectivity

Vision List Digest: Article 9, Volume 14, Issue 35
From: ronse@dpt-info.u-strasbg.fr
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**

Set-theoretical algebraic approaches to connectivity
in continuous or digital spaces

Christian Ronse

Rapport 95/13

LSIIT - URA 1871
Universite Louis Pasteur

ABSTRACT: Connectivity has been defined in the framework of topological
spaces, but also in graphs; the two types of definitions are not always
compatible. Serra gave a set of formal axioms for connectivity, which
consists in a list of properties of the family of all connected subsets of
a space; this definition includes as particular case connected sets in a
topological space or in a graph. He gave an equivalent characterization of
connectivity in terms of the properties of the operator associating to a
subset and a point of that space, the connected component of that subset
containing that point. In this paper we give another family of axioms,
equivalent to those of Serra, where connectivity is characterized in terms
of separating pairs of sets. In the case of graphs, where connected sets
are generated by pairs of end-vertices of edges, this new set of axioms is
equivalent to the separation axioms given by Haralick.


Christian Ronse ronse@dpt-info.u-strasbg.fr
http://dpt-info.u-strasbg.fr/~ronse/

LSIIT - URA 1871
Universite Louis Pasteur
UFR de Mathematique et Informatique
7 rue Rene Descartes Tel. (33) 88.41.66.38
F-67000 Strasbourg Fax. (33) 88.61.90.69

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