Net convergence structures with applications to vector lattices

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dc.contributor.author O’Brien, M.
dc.contributor.author Troitsky, V.G.
dc.contributor.author Van der Walt, Jan Harm
dc.date.accessioned 2023-01-26T04:42:23Z
dc.date.available 2023-01-26T04:42:23Z
dc.date.issued 2023
dc.description.abstract Convergence is a fundamental topic in analysis that is most commonly modeled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable functions and order convergence of nets in vector lattices. The theory of convergence structures provides a framework for studying more general modes of convergence. It also has one particularly striking feature: it is formalized using the language of filters. This paper develops a general theory of convergence in terms of nets. We show that it is equivalent to the filter-based theory and present some translations between the two areas. In particular, we provide a characterization of pretopological convergence structures in terms of nets. We also use our results to unify certain topics in vector lattices with general convergence theory. en_US
dc.description.department Mathematics and Applied Mathematics en_US
dc.description.librarian hj2023 en_US
dc.description.sponsorship NSERC grant. en_US
dc.description.uri https://www.tandfonline.com/loi/tqma20 en_US
dc.identifier.citation M. O’Brien, V.G. Troitsky & J.H. van der Walt (2023): Net convergence structures with applications to vector lattices, Quaestiones Mathematicae, 46(2): 243–280, DOI: 10.2989/16073606.2021.2012721. en_US
dc.identifier.issn 1607-3606 (print)
dc.identifier.issn 1727-933X (online)
dc.identifier.other 10.2989/16073606.2021.2012721
dc.identifier.uri https://repository.up.ac.za/handle/2263/88964
dc.language.iso en en_US
dc.publisher NISC (Pty) Ltd and Informa UK Limited (trading as Taylor & Francis Group) en_US
dc.rights © 2022 NISC (Pty) Ltd. This is an electronic version of an article published in Quaestiones Mathematicae, vol. 46, no. 2, pp. 243-280, 2023. doi : 10.2989/16073606.2021.2012721. Quaestiones Mathematicae is available online at: https://www.tandfonline.com/loi/tqma20. en_US
dc.subject Convergence structures en_US
dc.subject Nets and filters en_US
dc.subject Vector lattices en_US
dc.title Net convergence structures with applications to vector lattices en_US
dc.type Preprint Article en_US


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