Saturated set with respect to a function

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Definition

Let $X$ and $Y$ are sets and let $f:X\rightarrow Y$ be any function between them. A subset of $X$, $U\in\mathcal{P}(X)$, is said to be saturated with respect to $f$ if:

• $\exists V\in\mathcal{P}(Y)[U=f^{-1}(V)]$, in words:
  • There exists a subset of $Y$, $V$, such that $V$ is exactly the pre-image of $U$ under $f$

See next

• Equivalent conditions to a set being saturated with respect to a map

See also

• Fibre - this (saturated set) is a generalisation of a fibre.