Uniform continuity in sequentially uniform spaces (Q1332960)

The authors prove that every uniformly sequential uniform space is proximally fine, i.e., it is the finest uniform space inducing its proximity (no references to this result are given; it was proved e.g. by \textit{N. S. Ramm} and \textit{A. S. Shvarts} [Mat. Sb., Nov. Ser. 33(75), 157-180 (1952; Zbl 0050.391)]). Two consequences are given describing when a uniformly sequential space is topologically fine (both consequences, except the fourth condition in the second one, are valid for any proximally fine space).