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dc.contributor.author | O’Brien, M.![]() |
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dc.contributor.author | Troitsky, V.G.![]() |
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dc.contributor.author | Van der Walt, Jan Harm![]() |
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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 |