ABS: Egghe, Properties of topologies of information retrieval systems
gwhitney at UTKUX.UTCC.UTK.EDU
Tue Jun 13 18:14:55 EDT 2000
Author e-mail: leo.egghe at luc.ac.be
AU Egghe, L
TI Properties of topologies of information retrieval systems
SO MATHEMATICAL AND COMPUTER MODELLING
PU PERGAMON-ELSEVIER SCIENCE LTD
C1 Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium.
Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium.
Univ Instelling Antwerp, B-2610 Wilrijk, Belgium.
DE topology; IR-system; similarity; separation; connectedness;
AB This paper studies topological properties of different
topologies that are possible on the space of documents as they
are induced by queries in a query space together with a
similarity function between queries and documents. The main
topologies studied here are the retrieval topology (introduced
by Everett and Cater) and the similarity topology (introduced
by Egghe and Rousseau). The studied properties are the
separation properties T-0, T-1, and T-2 (Hausdorff), proximity
and connectedness. Full characterizations are given for the
diverse topologies to be T-0, T-1 or T-2. It is shown that the
retrieval topology is not necessarily a proximity space, while
the similarity topology and the pseudo-metric topology always
are proximity spaces. A characterization of connectedness in
terms of the Boolean NOT-operator is given, hereby showing the
intimate relationship between IR and topology.
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JI Math. Comput. Model.
RP Egghe L
Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium.
J9 MATH COMPUT MODELLING
PA THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB,
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