The free Banach lattice generated by a lattice
Antonio Avil\'es, Jos\'e David Rodr\'iguez Abell\'an
TL;DR
This paper introduces and explicitly constructs the free Banach lattice generated by a given lattice, exploring its properties especially when the lattice is a linear order, such as the countable chain condition.
Contribution
It provides an explicit description of the free Banach lattice generated by a lattice and investigates its properties in specific cases like linear orders.
Findings
Explicit construction of the free Banach lattice from a lattice
Analysis of properties like the countable chain condition in specific cases
Foundation for further study of Banach lattices generated by lattices
Abstract
We introduce the free Banach lattice generated by a lattice L. We give an explicit description of it and we study some of its properties for the case when is a linear order, like the countable chain condition.
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