Let ${(e_{\beta }:𝐐\to Y_{\beta })}_{\beta \in \mathbf{\text{Ord}}}$ be the large source of epimorphisms in the category $\mathbf{\text{Ury}}$ of Urysohn spaces constructed in [2]. A sink ${(g_{\beta }:Y_{\beta }\to X)}_{\beta \in \mathbf{\text{Ord}}}$ is called natural, if $g_{\beta }\circ e_{\beta }=g_{{\beta }^{\text{'}}}\circ e_{{\beta }^{\text{'}}}$ for all $\beta ,{\beta }^{\text{'}}\in \mathbf{\text{Ord}}$. In this paper natural sinks are characterized. As a result it is shown that $\mathbf{\text{Ury}}$ permits no $(Epi,ℳ)$-factorization structure for arbitrary (large) sources.

In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.