Definition:Invariant Subset
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It has been suggested that this page or section be merged into Definition:Positively Invariant Set of a Map. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mergeto}} from the code. |
It has been suggested that this page or section be merged into Definition:Invariant Set of a Map. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mergeto}} from the code. |
Definition
Let $S$ be a set.
Let $T \subseteq S$ be a subset of $S$.
Let $f: S \to S$ be a self-map on $S$.
Then $T$ is invariant under $f$ if and only if:
- $\forall t \in T: \map f t \in T$
Sources
- 1991: Gertrude Ehrlich: Fundamental Concepts of Abstract Algebra: $\S 2$: Definition $2.11.2$