Changes

Other names for the same concept are the ''fiber'', ''level set'', or ''pre-image'' of 1 under the mapping <math>f : X \to \mathbb{B}.\!</math>

Other names for the same concept are the ''fiber'', ''level set'', or ''pre-image'' of 1 under the mapping <math>f : X \to \mathbb{B}.\!</math>

Obviously, the relation between these operations is such that the following equations hold.

Obviously, the relation between these operations is such that:

S##  = S    and   f##  = f.

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(A^\sharp)_\flat = A & \text{and} & (f_\flat)^\sharp = f.

It will facilitate future discussions to explicitly go through the details of applying these selective operations to the case of n place relations.  If R c X1x...xXn is an n place relation, then R# : X1x...xXn  > B is the selector of R defined by:

It will facilitate future discussions to go through the details of applying these selective operations to the case of <math>n\!</math>-place relations.  If <math>L \subseteq X_1 \times \ldots \times X_n\!</math> is an <math>n\!</math>-place relation, then <math>L^\sharp : X_1 \times \ldots \times X_n \to \mathbb{B}\!</math> is the selector of <math>L\!</math> defined as follows.

R#(<x1, ... , xn>) = 1 iff <x1, ... , xn> C R.

</pre>

L^\sharp (x_1, \ldots, x_n) = 1 & \iff & (x_1, \ldots, x_n) \in L.

\end{array}</math>

===6.33. Sign Relational Complexes===

===6.33. Sign Relational Complexes===