Changes

Among the variety of conceivable regularities affecting 2-adic relations, we pay special attention to the <math>c\!</math>-regularity conditions where <math>c\!</math> is equal to 1.

Among the variety of conceivable regularities affecting 2-adic relations, we pay special attention to the <math>c\!</math>-regularity conditions where <math>c\!</math> is equal to 1.

Let <math>L \subseteq X \times Y\!</math> be an arbitrary 2-adic relation.  The following properties of <math>L\!</math> can be defined:

Let <math>L \subseteq X \times Y\!</math> be an arbitrary 2-adic relation.  The following properties of <math>L\!</math> can then be defined:

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We have already looked at 2-adic relations that separately exemplify each of these regularities.  We also introduced a few bits of additional terminology and special-purpose notations for working with tubular relations:

We have already looked at 2-adic relations that separately exemplify each of these regularities.  We also introduced a few bits of additional terminology and special-purpose notations for working with tubular relations:

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<math>\begin{array}{lll}

<math>\begin{array}{lll}

P ~\text{is a pre-function}~ P : X \rightharpoonup Y

L ~\text{is a pre-function}~ L : X \rightharpoonup Y

& \iff &

& \iff &

P ~\text{is tubular at}~ X.

L ~\text{is tubular at}~ X.

\\[6pt]

\\[6pt]

P ~\text{is a pre-function}~ P : X \leftharpoonup Y

L ~\text{is a pre-function}~ L : X \leftharpoonup Y

& \iff &

& \iff &

P ~\text{is tubular at}~ Y.

L ~\text{is tubular at}~ Y.

\end{array}</math>

\end{array}</math>

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