Fibre

Stub grade: A

This page is a stub

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:

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

Definition

Let [ilmath]f:X\rightarrow Y[/ilmath] be a function, then:

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

See also

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