@article{Elfard_2015, title={Free paratopological groups}, volume={16}, url={https://polipapers.upv.es/index.php/AGT/article/view/1874}, DOI={10.4995/agt.2015.1874}, abstractNote={Let FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X) on a $P_\alpha$-space $X$ where $\alpha$ is an infinite cardinal and then we prove that the group FP(X) is an Alexandroff space if X is an Alexandroff space. Moreover, we introduce a~neighborhood base at the identity of the group FP(X) when the space X is Alexandroff and then we give some properties of this neighborhood base. As applications of these, we prove that the group FP(X) is T_0 if X is T_0, we characterize the spaces X for which the group FP(X) is a topological group and then we give a class of spaces $X$ for which the group FP(X) has the inductive limit property.}, number={2}, journal={Applied General Topology}, author={Elfard, Ali Sayed}, year={2015}, month={Oct.}, pages={89–98} }