On p.371 of "The Joy of Cats", by J.Adamek H.Herrlich and G.E.Strecker:

Proposition 21.32

If a topological category $(\mathbf{A},U)$ is a finally dense full concrete subcategory of $(\mathbf{B},V)$, then $(\mathbf{A},U)$ is concretely reflective in $(\mathbf{B},V)$.

Is a concretely reflective full concrete subcategory necessarily finally dense?

Added: I recall that $(\mathbf{A},U)$ is finally dense in $(\mathbf{B},V)$ iff for each object $B\in\mathbf{B}$ there is a final sink $(f_i\colon A_i\to B)_{i\in I}$ in $\mathbf{B}$ with all $A_i\in\mathbf{A}$.