Topological Aspects of Information Retrieval

Let (DS, QS, sim) be a retrieval system consisting of a document space DS, a query space QS, and a function sim, expressing the similarity between a document and a query. Following Everett and Cater, we introduce topologies on the document space. These topologies are generated by the similarity function sim and the query space QS. Three topolgies will be studied : the retrieval topology, the similarity topology and the (pseudo-)metric one. It is shown that the retrieval topology is the coarsest of the three, while the (pseudo-)metric is the strongest. These three topologies are in general different, reflecting distinct topological aspects of information retrieval. We present necessary and sufficient conditions for these topological to be equal. LUC, Universitaire Campus, B-3590 Diepenbeek, Belgium and UIA, Universiteitsplein 1, B-2610 Wilrijk, Belgium E-mail : [email protected] UIA, Universiteitsplein 1, B-2610 Wilrijk, Belgium and KHBO, Zeedijk 101, B-8400 Oostende, Belgium E-mail : [email protected]