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http://hdl.handle.net/1942/804
Title: | Properties of topologies of information retrieval systems | Authors: | EGGHE, Leo | Issue Date: | 1998 | Publisher: | Elsevier | Source: | Mathematical and Computer Modelling, 27(2). p. 61-79 | Abstract: | 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 T0, T1, and T2 (Hausdorff), proximity and connectedness. Full characterizations are given for the diverse topologies to be T0, T1, or T2. 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. | Keywords: | topology; IR-system; similarity; separation; connectedness; proximity | Document URI: | http://hdl.handle.net/1942/804 | ISSN: | 0895-7177 | DOI: | 10.1016/S0895-7177(97)00260-4 | ISI #: | 000072245000004 | Type: | Journal Contribution | Validations: | ecoom 1999 |
Appears in Collections: | Research publications |
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File | Description | Size | Format | |
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properties.pdf | Peer-reviewed author version | 603.6 kB | Adobe PDF | View/Open |
systems 1.pdf | Published version | 1.24 MB | Adobe PDF | View/Open |
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