Characterizing s-paratopological groups by free paratopological groups

A paratopological group G is called an s-paratopological group if every sequentially continuous homomorphism from G to a paratopological group is continuous. In this paper, the structure of s-paratopological groups is established in terms of free paratopological groups. Namely, if G is a non-discrete T1 paratopological group, then the following statements (1), (2), (3) and (4) are equivalent. (1) G is an s-paratopological group. (2) G is topologically isomorphic to a quotient group of a free paratopological group on a metrizable space. (3) G is topologically isomorphic to a quotient group of a free paratopological group on a T1 Fréchet space. (4) G is topologically isomorphic to a quotient group of a free paratopological group on a T1 sequential space.