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In a digraph $D = (X, \mathcal{U})$, not necessarily finite, an arc $(x, y)\in \mathcal{U}$ is reachable from a vertex $u$ if there exists a directed walk$W$ that originates from $u$ and contains $(x, y)$. A subset $S \subseteq X$ isan arc-reaching set of $D$ if for every arc $(x, y)$ there exists a diwalk $W$originating at a vertex $u \in S$ and containing $(x, y)$. A minimalarc-reaching set is an arc-basis. $S$ is a point-reaching set if for everyvertex $v$ there exists a diwalk $W$ to $v$ originating at a vertex $u \in S$.A minimal point-reaching set is a point-basis. We extend the results of Harary,Norman, and Cartwright on point-bases in finite digraphs to point- andarc-bases in infinite digraphs.

Point- and arc-reaching sets of vertices in a digraph