Di Concilio, Anna Proximity: a powerful tool in extension theory, function spaces, hyperspaces, boolean algebras and point-free geometry. (English) Zbl 1192.54010 Mynard, Frédéric (ed.) et al., Beyond topology. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4279-9/pbk). Contemporary Mathematics 486, 89-114 (2009). The article serves as a brief survey of the theory of proximity spaces and their usage in topology. Description and discussion of proximity axioms is provided, then inducing topologies, relations to uniformities and Smirnov compactifications follow, locally compact hulls are presented in more or less details. Finally, some applications to function spaces (mainly convergence), homeomorphism groups and to hyperspaces are given (connections to lattices and point-free geometry are briefly discussed, too).For the entire collection see [Zbl 1165.54001]. Reviewer: Miroslav Hušek (Praha) Cited in 1 ReviewCited in 19 Documents MSC: 54E05 Proximity structures and generalizations 54B20 Hyperspaces in general topology 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54-02 Research exposition (monographs, survey articles) pertaining to general topology Keywords:proximity space; compactification; uniform space PDFBibTeX XMLCite \textit{A. Di Concilio}, Contemp. Math. 486, 89--114 (2009; Zbl 1192.54010)