Free uniformly complete vector lattices
Eduard Emelyanov, Svetlana Gorokhova
TL;DR
This paper introduces the concept of a free uniformly complete vector lattice generated by a set, providing a concrete representation as a space of continuous positively homogeneous functions.
Contribution
It defines the free uniformly complete vector lattice and offers a concrete functional representation, advancing the theoretical understanding of such structures.
Findings
Defined the free uniformly complete vector lattice.
Provided a concrete representation as continuous positively homogeneous functions.
Enhanced the theoretical framework of vector lattices.
Abstract
We define a free uniformly complete vector lattice over a set of generators and give its concrete representation as a space of continuous positively homogeneous functions.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topology and Set Theory · Rings, Modules, and Algebras