\begin{definition}[Definition:Magma of Sets]
Let $X$ be a set.
Let $\SS \subseteq \powerset X$ be a set of subsets of $X$.
Let $I$ be an index set.
For every $i \in I$, let $J_i$ be an index set, and let:
:$\phi_i: \powerset X^{J_i} \to \powerset X$
be a partial mapping.
Then $\SS$ is a '''magma of sets for $\set {\phi_i: i \in I}$ on $X$''' {{iff}}:
:$\forall i \in I: \map {\phi_i} {\family {S_j}_{j \mathop \in J_i} } \in \SS$
for every indexed family $\family {S_j}_{j \mathop \in J_i} \in \SS^{J_i}$ in the domain of $\phi$.
That is, {{iff}} $\SS$ is closed under $\phi_i$ for all $i \in I$.
{{improve|Dispose of the index set to prevent problems on Topology as Magma of Sets, where $I$ would be a proper class}}
\end{definition}