A regular space without a uniformly regular quasi-uniformity (Q2639373)

We point out that a construction due to \textit{J. Vaughan} [Proc. Am. Math. Soc. 75, 339-342 (1979; Zbl 0412.54023)] yields an example of a regular \(T_ 1\)-space that does not admit a uniformly regular quasi-uniformity. Since each quiet quasi-uniformity is uniformly regular, it follows that the question of \textit{P. Fletcher}, \textit{J. Hejcman} and \textit{W. Hunsaker} [ibid. 108, No.4, 1077-1079 (1990; Zbl 0689.54018)] whether each regular \(T_ 1\)-space admits a quiet quasi-uniformity has a negative answer.