Towards a theory of unbounded locally solid Riesz spaces

TL;DR

This paper introduces the concept of unbounded locally solid Riesz spaces, exploring their fundamental properties to advance the theoretical understanding of these mathematical structures.

Contribution

It presents the first formal definition of unbounded locally solid Riesz spaces and investigates their core properties.

Findings

Defined unbounded locally solid Riesz spaces.

Established basic properties and structure theorems.

Laid groundwork for further research in this area.

Abstract

We introduce the notion of unbounded locally solid Riesz spaces, and investigate its fundamental properties.