Definition:Maximal/Set
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Definition
Let $S$ be a set.
Let $\powerset S$ be the power set of $S$.
Let $\TT \subseteq \powerset S$ be a subset of $\powerset S$.
Let $\struct {\TT, \subseteq}$ be the ordered set formed on $\TT$ by $\subseteq$ considered as an ordering.
Then $T \in \TT$ is a maximal set of $\TT$ if and only if $T$ is a maximal element of $\struct {\TT, \subseteq}$.
That is:
- $\forall X \in \TT: T \subseteq X \implies T = X$
Also see
Sources
- 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation