Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)

Demonstrates how recall and precision can be expressed using a topological approach to retrieval introduced by S.C. Cater (1986); investigates threshold and close match retrieval systems and optimal and non-optimal searching; and highlights relations with hypergeometric and non-standard distributions. Includes seven appendices of mathematical…

Demonstrates that if the similarity function of a retrieval system leads to a (pseudo-) metric, the retrieval, similarity and Everett-Cater metric topology coincide and are different from the discrete topology; this is the case if documents are represented by lists, using the Jaccard similarity measure. The corresponding metric is the…