A characterization of Tychonoff spaces with applications to paratopological groups

We prove that a regular topological space $X$ is Tychonoff if and only if its topology is generated by a quasi-uniformity $\U$ such that for every $U\in\U$ and $A\subset X$ there is $V\in\U$ such that $B(\bar A,V)\subset\overline{B(A,U)}$. This characterization implies that each regular paratopological group is Tychonoff and each Hausdorff paratopological group is functionally Hausdorff. This resolves two old problems in the theory of paratopological groups, which stood open for more than 50 years. More details can be found in the paper (http://arxiv.org/abs/1410.1504) written jointly with Alex Ravsky.