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Revision as of 05:10, 10 February 2009
, 05:10, 10 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 13
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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 SxI:
| width="20%" | <math>\operatorname{Definition~13}</math>
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D13a. DerR
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D13b. Der(R)
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D13c. {<x,y> C SxI : DenR|x = DenR|y}
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| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
D13d. {<x,y> C SxI : Den(R, x) = Den(R, y)}
| width="80%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math>
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|- style="height:40px"
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| <math>\text{then}\!</math>
| <math>\text{the following are identical subsets of}~ S \times I \, :</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{D13a.}</math>
| width="80%" style="border-top:1px solid black" | <math>\operatorname{Der}^L</math>
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| <math>\operatorname{D13b.}</math>
| <math>\operatorname{Der}(L)</math>
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| <math>\operatorname{D13c.}</math>
| <math>\{ (x, y) \in S \times I ~:~ \operatorname{Den}^L|_x = \operatorname{Den}^L|_y \}</math>
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| <math>\operatorname{D13d.}</math>
| <math>\{ (x, y) \in S \times I ~:~ \operatorname{Den}(L, x) = \operatorname{Den}(L, y) \}</math>
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