Neighborhood base at the identity of free paratopological groups

TL;DR

This paper extends Pestov's description of neighborhood bases at the identity from free topological groups to free paratopological groups, using fine quasi-uniformities, and explores their properties.

Contribution

It provides an analogue of Pestov's description for free paratopological groups and investigates their structural properties.

Findings

Derived a neighborhood base description for free paratopological groups

Compared properties of Markov and Graev free paratopological groups

Established connections with fine quasi-uniformities

Abstract

V. G. Pestov described a neighborhood base at the identity of the Markov free topological group $F(X)$ on a Tychonoff space $X$ in terms of the fine uniformity on $X$. In this paper, an analogue of Pestov's description for the Markov free paratopological group $\FP(X)$ on a space $X$ in terms of the fine quasi-uniformity on $X$ is found and some properties of the Markov and Graev free paratopological groups are presented.