A space $X$ is called $CCS$-normal space if there exist a normal space $Y$ and a bijection $f: Xmapsto Y$ such that $flvert_C:Cmapsto f(C)$ is homeomorphism for any cellular-compact subset $C$ of $X$. We discuss about the relations between $C$-normal, $CC$-normal, $Ps$-normal spaces with $CCS$-normal.
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