Category:Magmas of Sets

This category contains results about Magmas of Sets.
Definitions specific to this category can be found in Definitions/Magmas 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 $X$ if and only if:

$\forall i \in I: \map {\phi_i} {\family {S_j}_{j \mathop \in J_i} } \in \SS$

for every indexed family $\family {S_j}_{j \mathop \in J_i} \in \SS^{J_i}$ in the domain of $\phi$.