# Equivalent conditions to a set being saturated with respect to a function

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## Contents

## Statement

Let [ilmath]X[/ilmath] and [ilmath]Y[/ilmath] be sets and let [ilmath]f:X\rightarrow Y[/ilmath] be a function. Let [ilmath]U\in\mathcal{P}(X)[/ilmath] be an arbitrary subset of [ilmath]X[/ilmath], then^{[1]}:

- [ilmath]U[/ilmath] is saturated with respect to [ilmath]f[/ilmath]

- Any one (or more) of the following:

## Proof

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Easy work, routine

**This proof has been marked as an page requiring an easy proof**## Notes

## References

- ↑
^{1.0}^{1.1}^{1.2}^{1.3}Introduction to Topological Manifolds - John M. Lee