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Returning to dyadic relations, it is useful to describe some familiar classes of objects in terms of their local and numerical incidence properties. Let <math>L \subseteq S \times T\!</math> be an arbitrary dyadic relation. The following properties of <math>L\!</math> can then be defined.
Returning to dyadic relations, it is useful to describe some familiar classes of objects in terms of their local and numerical incidence properties. Let <math>L \subseteq X \times Y\!</math> be an arbitrary dyadic relation. The following properties of <math>L\!</math> can then be defined.
{| align="center" cellspacing="8" width="90%"
|
<math>\begin{array}{lll}
L ~\text{is total at}~ X
& \iff &
L ~\text{is}~ (\ge 1)\text{-regular}~ \text{at}~ X.
\\[6pt]
L ~\text{is total at}~ Y
& \iff &
L ~\text{is}~ (\ge 1)\text{-regular}~ \text{at}~ Y.
\\[6pt]
L ~\text{is tubular at}~ X
& \iff &
L ~\text{is}~ (\le 1)\text{-regular}~ \text{at}~ X.
\\[6pt]
L ~\text{is tubular at}~ Y
& \iff &
L ~\text{is}~ (\le 1)\text{-regular}~ \text{at}~ Y.
\end{array}</math>
|}
<pre>
<pre>
If R is tubular at S, then R is called a "partial function" or "prefunction" from S to T, often indicated by writing R = p : S ~> T.
If R is tubular at S, then R is called a "partial function" or "prefunction" from S to T, often indicated by writing R = p : S ~> T.
