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Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology. (English) Zbl 1002.54002
Aull, C. E. (ed.) et al., Handbook of the history of general topology. Volume 3. Papers from the special session of the American Mathematical Society meeting, San Antonio, TX, USA, 1993. Dordrecht: Kluwer Academic Publishers. Hist. Topol. 3, 853-968 (2001).
This article studies the history of asymmetric topology, and “with the exception of Lowen’s approach spaces, which is an especially important concept $\cdots$, concentrates on quasiuniformities and quasi-metrics”. The coherent presentation and organization of this history could have been achieved only by someone with the author’s encyclopedic knowledge of the subject, and his article will prove invaluable both to mathematical historians and to researchers. Firstly, although the author did not attempt to obtain a complete list of articles published in the area of asymmetric topology, the bibliography is extensive (it has nearly 600 entries). Secondly, without intruding upon the history of asymmetric topology, the author has indicated where this history is incomplete because of interesting outstanding problems. Thus the reader is given the necessary references, the guidance and the motivation to help fulfill the author’s promise that “in the years to come $\cdots$ many new and surprising results [in assymetric topology] will still be detected and published”.

##### MSC:
 54-03 Historical (general topology) 54E15 Uniform structures and generalizations
##### Keywords:
quasi-uniformity; quasi-metric