A subcategory $\mathcal{C}$ of the category $Top$ of topological spaces is a [reflective subcategory](http://en.wikipedia.org/wiki/Reflective_subcategory) if the inclusion functor $i:\mathcal{C}\hookrightarrow Top$ has a left adjoint $R:Top\rightarrow \mathcal{C}$. In other words, for every space $X$, there is a space $RX\in \mathcal{C}$ and a map $r:X\rightarrow RX$ such that for each map $f:X \rightarrow Y$ with $Y\in \mathcal{C}$, there is a unique map $\tilde{f}:RX\rightarrow Y$ such that $\tilde{f}\circ r=f$.

If the reflection map $r$ is always a quotient map, $\mathcal{C}$ is said to be a quotient-reflective subcategory. For example, it seems that the subcategories of $T\_0$ spaces and $T\_2$ spaces are quotient-reflective but the subcategories of completely regular spaces and compact Hausdorff spaces are reflective but not quotient-reflective. I'd like to hear of other examples of quotient-reflective subcategories as well.

There seem to be conditions fully characterizing when a subcategory is reflective. For example, some necessary conditions are mentioned in the answer to this MO [question](https://mathoverflow.net/questions/9504/why-is-top-4-a-reflective-subcategory-of-top-3). Are there also conditions characterizing subcategories which are quotient-reflective?