Multiplication is an open bilinear mapping in the Banach algebra of functions of bounded Wiener p-variation

Let $B{V}_p[0,1]$, $1\le p<\mathrm{\infty }$, be the Banach algebra of functions of bounded $p$-variation in the sense of Wiener. Recently, Kowalczyk and Turowska \cite{KT19} proved that the multiplication in $B{V}_1[0,1]$ is an open bilinear mapping. We extend this result for all values of $p\in [1,\mathrm{\infty })$.