A topology $R(\tau)$ is contructed from a given topolgy $\tau$ on a set $X$ . $R(\tau)$ is coarser than $\tau$, and the following are some results based on this topology:
1. Continuity and RS-continuity are equivalent if the codomain is re topologized by $R(\tau)$.
2. The class of semi-open sets with respect to $R(\tau)$ is a topology.
3. $T_2$ and semi-$T_2$ properties are equivalent on a space whose topology is $R(\tau)$.
4. Minimal $R_0$-spaces are RS-compact: