The source number of a Tychonoff space in its compactifications

The source number $so(X)$ of a Tychonoff space $X$ denotes the minimal cardinal $\tau$ such that $X$ has an open source $\mathcal{S}$ in some compactification $bX$ for which $|\mathcal{S}|\le \tau$. In this paper some properties of source numbers are studied. Among other things, we showed that the equalities $w(X)=nw(X)so(X)$ and $w(X)=so(X)Nag(X)iw(X)$ hold for every Tychonoff space $X$, where $w(X)$, $nw(X)$, $iw(X)$, $Nag(X)$ denote the weight, network weight, $i$-weight, and Nagami number of a space $X$, respectively. Some corollaries about the two statements were obtained.