o-Tightness in paratopological groups

In this paper, we mainly discuss the o-tightness in paratopological groups. The following results are obtained: (1) Every paratopological group H satisfying Sm(H)⋅get(H)≤ω is Gδ-preserving. (2) The o-tightness of the product space X×H is countable for every Hausdorff feathered paratopological group H and every space X with ot(X)≤ω. As an application, we deduce that every Hausdorff feathered paratopological group H has countable o-tightness; in particular, H is a Moscow space, which gives a positive answer to [2, Open problem 6.4.8].