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Revision as of 15:14, 9 February 2009
, 15:14, 9 February 2009→Derived Equivalence Relations: format definition box
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
Definition 10
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
If R c OxSxI,
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then the following are identical subsets of OxS:
| width="20%" | <math>\operatorname{Definition~10}</math>
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D10a. ROS
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D10b. DenR
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D10c. Den(R)
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| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
D10d. PrOS(R)
| width="80%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math>
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D10e. {<o, s> C OxS : <o, s, i> C R for some i C I}
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| <math>\text{then}\!</math>
| <math>\text{the following are identical subsets of}~ O \times S \, :</math>
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{D10a.}</math>
| width="80%" style="border-top:1px solid black" | <math>L_{OS}\!</math>
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| <math>\operatorname{D10b.}</math>
| <math>\operatorname{Den}^L</math>
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| <math>\operatorname{D10c.}</math>
| <math>\operatorname{Den}(L)</math>
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| <math>\operatorname{D10d.}</math>
| <math>\operatorname{proj}_{OS}(L)</math>
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| <math>\operatorname{D10e.}</math>
| <math>\{ (o, s) \in O \times S ~:~ (o, s, i) \in L ~\operatorname{for~some}~ i \in I \}</math>
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