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RELATIVE UNIFORM CONVERGENCE IN VECTOR LATTICES: ODDS AND ENDS

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Abstract

Conditions under which the relatively uniform convergence in vector lattices is complete, topological, and agrees with the order convergence are presented. r-Completion of an Archimedean vector lattice is investigated. Basic properties of the Archimedization of a vector lattice are established.

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Funding

The research was supported by the State Task to the Sobolev Institute of Mathematics (Project FWNF-2022-0004).

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  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Eduard Emelyanov

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  1. Eduard Emelyanov
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Correspondence to Eduard Emelyanov.

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Dedicated to Professor A. G. Kusraev on occasion of his 70th birthday.

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Emelyanov, E. RELATIVE UNIFORM CONVERGENCE IN VECTOR LATTICES: ODDS AND ENDS. J Math Sci 271, 733–742 (2023). https://doi.org/10.1007/s10958-023-06637-1

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