Co-Rs-Compact Topologies

Abstract


 
 
 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: