A characterization of $\sigma $-compactness of a cosmic space $X$ by means of subspaces of $R^X$
A characterization of $\sigma $-compactness of a cosmic space $X$ by means of subspaces of $R^X$
This work is devoted to the relationship between topological properties of a space $X$ and those of $C_{p}(X)$ (= the space of continuous real-valued functions on $X$, with the topology of pointwise convergence). The emphasis is on $\sigma$-compactness of $X$ and on location of $C_{p}(X)$ in $R^{X}$. In particular, $\sigma$-compact …