| ABSTRACT TOPOLOGICAL ASPECTS OF INFORMATION RETRIEVAL (2008) | |||||||||||||||
Abstract | |||||||||||||||
| 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. | |||||||||||||||
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