Definition:Boolean Fiber

Let $$\mathbb{B} = \left\{{T, F}\right\}$$ be a boolean domain.

Let $$f : X \to \mathbb{B}$$ be a boolean-valued function.

Then $$f$$ has two fibers:
 * The fiber of $$F$$ under $$f\!$$, defined as $$f^{-1} \left({F}\right) = \left\{{x \in X: f \left({x}\right) = F}\right\}$$;
 * The fiber of $$T$$ under $$f\!$$, defined as $$f^{-1} \left({T}\right) = \left\{{x \in X: f \left({x}\right) = T}\right\}$$.

These fibers are called boolean fibers.

The fiber of $$T$$ is known as the fiber of truth.