Neighborhood base at the identity of free paratopological groups

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.