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Revision as of 17:08, 12 April 2009
, 17:08, 12 April 2009→Commentary Note 11.6
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+Let ''P'' ⊆ ''X'' × ''Y'' be an arbitrary 2-adic relation. The following properties of ''P'' can be defined:
−:{| cellpadding="6"
−| ''P'' is "total" at ''X''
−| iff
−| ''P'' is (≥1)-regular at ''X''.
−|-
−| ''P'' is "total" at ''Y''
−| iff
−| ''P'' is (≥1)-regular at ''Y''.
−|-
−| ''P'' is "tubular" at ''X''
−| iff
−| ''P'' is (≤1)-regular at ''X''.
−|-
−| ''P'' is "tubular" at ''Y''
−| iff
−| ''P'' is (≤1)-regular at ''Y''.
−|}
−|}
−''E''<sub>1</sub> exemplifies the quality of "totality at ''X''".
−''E''<sub>2</sub> exemplifies the quality of "totality at ''Y''".+''E''<sub>3</sub> exemplifies the quality of "tubularity at ''X''".+''E''<sub>4</sub> exemplifies the quality of "tubularity at ''Y''".+
===Commentary Note 11.6===
===Commentary Note 11.6===
−Let's continue to work our way through the rest of the first set of definitions, making up appropriate examples as we go.
+Let's continue working our way through the above definitions, constructing appropriate examples as we go.
−{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
+<math>E_1\!</math> exemplifies the quality of ''totality at <math>X.\!</math>''
+{| align="center" cellspacing="6" width="90%"
|
|
−<pre>
<pre>
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
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0 1 2 3 4 5 6 7 8 9
</pre>
</pre>
+|}
−<math>E_2\!</math> exemplifies the quality of ''totality at <math>Y.\!</math>''
+{| align="center" cellspacing="6" width="90%"
+|
<pre>
<pre>
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
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0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
</pre>
</pre>
+|}
−<math>E_3\!</math> exemplifies the quality of ''tubularity at <math>X.\!</math>''
+{| align="center" cellspacing="6" width="90%"
+|
<pre>
<pre>
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
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0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
</pre>
</pre>
+|}
−<math>E_4\!</math> exemplifies the quality of ''tubularity at <math>Y.\!</math>''
+{| align="center" cellspacing="6" width="90%"
+|
<pre>
<pre>
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
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</pre>
</pre>
+|}
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
