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• W2967462807 abstract "Lebesgue topologies on Riesz spaces are topologies that are order continuous: every net that is order convergent to 0 converges to 0 in the topology. In this paper we give an overview of various types of Lebesgue topologies, replacing order convergent nets by nets that are unboundedly order convergent and bounded in some sense. In the case of order boundedness we obtain Lebesgue topologies as usually defined. In normed Riesz spaces, norm-boundedness can be used to define another class of Lebesgue topologies, the uniformly Lebesgue topologies. The relationship between these two types of Lebesgue topologies and the corresponding pre-Lebesgue topologies is investigated, as well as the role of unbounded Lebesgue topologies. We identify the finest uniformly Lebesgue topologies on a Banach lattice, and show that it may be regarded as a mixed topology, and that the coarsest Hausdorff Lebesgue topology also enters into the picture." @default.
• W2967462807 created "2019-08-22" @default.
• W2967462807 creator A5022763555 @default.
• W2967462807 date "2019-01-01" @default.
• W2967462807 modified "2023-09-27" @default.
• W2967462807 title "Lebesgue Topologies and Mixed Topologies" @default.
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• W2967462807 doi "https://doi.org/10.1007/978-3-030-10850-2_5" @default.
• W2967462807 hasPublicationYear "2019" @default.
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