In this paper we further investigate the results given in [9] and [10]. A space $X$ is HCC (hypercouniably compact) if every a-compact set in $X$ has the compact closure in $X$ (see [10]). A space $X$ is SCC(strongly countably compact) if every countable subset in $X$ has the compact closure in $X$ (see [6]). A pair $(Y,c)$ is called a SCC(HCC) extension of the space $X$ if $Y$ is a SCC(HCC) space and $c:X\to Y$ is a homeomorphic embeding of $X$ in $Y$ such that $cl_Y(c(X))=Y$. In section 2 we consider SCC and HCC extensions of locally compact spaces. In section 3 we also consider continuous images of HCC spaces.