  We show that the $\sigma$-product of complete Erd\H{o}s space $\mathfrak
E_{\mathrm{c}}$ is homeomorphic to the rational product $\mathbb Q\times
\mathfrak E_{\mathrm{c}}$, answering a question by Rodrigo
Hern\'{a}ndez-Guti\'{e}rrez and Alfredo Zaragoza.
