  In 1978, Kulli and Janakiram \citep{KulliJanakiramSplit} defined the split
dominating set: a dominating set $S$ of vertices in a graph $G = (V, E)$ is
called {\em split dominating} if the induced subgraph $\langle V \setminus
S\rangle$ is either disconnected or a $K_1$. In this paper we introduce the
properties split independence and split irredundance. A set $S$ of vertices in
a graph $G =(V,E)$ is called a {\em split independent set} if $S$ is
independent and the induced subgraph $\langle V \setminus S \rangle$ is either
disconnected or a $K_1$. A set $S$ of vertices in a graph $G = (V,E)$ is called
a {\em split irredundant set} if for $u \in S$, $u$ has a private neighbor with
respect to $V(S)$ and the induced subgraph $\langle V \setminus S\rangle$ is
either disconnected or a $K_1$.
