Regularity in polar spaces of infinite rank

TL;DR

This paper introduces a new definition of regularity for infinite rank polar spaces and explores how properties from finite rank cases extend to the infinite case.

Contribution

It proposes a suitable notion of regularity for infinite rank polar spaces and analyzes the generalization of finite rank properties.

Findings

Established a definition of regularity for infinite rank polar spaces

Analyzed the extent of property generalization from finite to infinite rank

Provided insights into structural similarities and differences

Abstract

In this paper we propose a definition of regularity suited for polar spaces of infinite rank and we investigate to which extent properties of regular polar spaces of finite rank can be generalized to polar spaces of infinite rank.