Affiliations: Department of Mathematics and Computer Science,
University of Sofia, Blvd. James Bourchier 5, 1126 Sofia, Bulgaria. E-mail:
{gdimov,dvak}@fmi.uni-sofia.bg
Abstract: This paper is the second part of the paper [2]. Both of themare in
the field of region-based (or Whitehedian) theory of space, which is an
important subfield of Qualitative Spatial Reasoning (QSR). The paper can be
considered also as an application of abstract algebra and topology to some
problems arising and motivated in Theoretical Computer Science and QSR. In [2],
different axiomatizations for region-based theory of space were given. The most
general one was introduced under the name "Contact Algebra". In this paper some
categories defined in the language of contact algebras are introduced. It is
shown that they are equivalent to the category of all semiregular
T_0-spaces and their continuous maps and to its full
subcategories having as objects all regular (respectively, completely regular;
compact; locally compact) Hausdorff spaces. An algorithm for a direct
construction of all, up to homeomorphism, finite semiregular
T_0-spaces of rank n is found. An example of an RCC model
which has no regular Hausdorff representation space is presented. The main
method of investigation in both parts is a lattice-theoretic generalization of
methods and constructions from the theory of proximity spaces. Proximity models
for various kinds of contact algebras are given here. In this way, the paper
can be regarded as a full realization of the proximity approach to the
region-based theory of space.
