Fibre

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Could use another reference. I know An Introduction to Algebraic Topology - Joseph J. Rotman defines this term!

Definition

Let $f:X\rightarrow Y$ be a function, then:

• A fibre of $f$ is any set of the form $f^{-1}(\{y\})$ for some $y\in Y$

See also

• Level set - a similar concept, rarely used in the same context as a fibre however
• Saturated - generalisation of fibre. $U\in\mathcal{P}(X)$ is saturated with respect to $f$ if there is a subset, $V\in\mathcal{P}(Y)$ such that $U=f^{-1}(V)$