A topology on the Fremlin tensor product of locally convex-solid vector lattices

TL;DR

This paper explores how to introduce a compatible topological structure to the Fremlin tensor product of locally convex-solid vector lattices, aiming to make it into a locally convex-solid vector lattice.

Contribution

It proposes a method to endow the Fremlin tensor product with a topology that preserves the locally convex-solid vector lattice structure.

Findings

Established a topological framework for E⊗F

Ensured the tensor product retains lattice properties

Provided conditions for the topology to be locally convex-solid

Abstract

Suppose E and F are locally convex-solid vector lattices. Although we have a suitable vector lattice structure for the tensor product E and F (known as the Fremlin tensor product and denoted by E\otimesF), there is a lack of topological structure on E\otimes F, in general. In this note, we consider a topological attitude on E\otimes F that makes it into a locally convex-solid vector lattice, as well.