Topology of document retrieval systems

Document‐retrieval systems can be classified on the basis of the topology each system induces on its set of possible documents. The induced topology measures closeness among documents, with two documents considered close if a retrieval which includes one document is likely to also include the other. The induced topology may be distinct from the usual topology which the set of documents inherits from its indexing system. Under a reasonably general definition of document‐retrieval systems, the existence of a query which returns one of two preselected documents, but not the other, is a necessary and sufficient condition for the document‐retrieval system to induce not only a topology, but also a metric on its set of documents. The topological structure and induced metric of the following document‐retrieval systems are analyzed: the vector‐space model, the fuzzyset model, the extended‐Boolean model, a probabilistic model, and the TIRS model. © 1992 John Wiley & Sons, Inc.