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Revision as of 17:46, 12 April 2009
, 17:46, 12 April 2009→Selection 11
& \iff &
& \iff &
P ~\text{is}~ (\le 1)\text{-regular}~ \text{at}~ Y.
P ~\text{is}~ (\le 1)\text{-regular}~ \text{at}~ Y.
\end{array}</math>
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If <math>P \subseteq X \times Y</math> is tubular at <math>X,\!</math> then <math>P\!</math> is known as a ''partial function'' or a ''pre-function'' from <math>X\!</math> to <math>Y,\!</math> frequently signalized by renaming <math>P\!</math> with an alternative lower case name, say <math>{}^{\backprime\backprime} p {}^{\prime\prime},</math> and writing <math>p : X \rightharpoonup Y.</math>
Just by way of formalizing the definition:
{| align="center" cellspacing="6" width="90%"
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<math>\begin{array}{lll}
P ~\text{is a pre-function}~ P : X \rightharpoonup Y
& \iff &
P ~\text{is tubular at}~ X.
\\[6pt]
P ~\text{is a pre-function}~ P : X \leftharpoonup Y
& \iff &
P ~\text{is tubular at}~ Y.
\end{array}</math>
\end{array}</math>
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</pre>
</pre>
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