\begin{definition}[Definition:Boolean Fiber]
Let $\Bbb B = \set {\T, \F}$ be a boolean domain.
Let $f : X \to \Bbb B$ be a boolean-valued function.
Then $f$ has two fibers:
:$(1): \quad$ The fiber of $\F$ under $f$, defined as $\map {f^{-1} } \F = \set {x \in X: \map f x = \F}$
:$(2): \quad$ The fiber of $\T$ under $f$, defined as $\map {f^{-1} } \T = \set {x \in X: \map f x = \T}$.
These fibers are called '''boolean fibers'''.
\end{definition}