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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 21:45, 9 February 2009
, 21:45, 9 February 2009→Definition 12
===Definition 12===
===Definition 12===
<br>
<br>
|- style="height:40px; text-align:center"
|- style="height:40px; text-align:center"
| width="80%" |
| width="80%" |
| width="20%" | <math>\operatorname{Definition~10}</math>
| width="20%" | <math>\operatorname{Definition~12}</math>
|}
|}
|-
|-
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="80%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math>
| width="80%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math>
|- style="height:40px"
|
| <math>\text{and}\!</math>
| <math>x ~\in~ S</math>
|- style="height:40px"
|- style="height:40px"
|
|
| <math>\text{then}\!</math>
| <math>\text{then}\!</math>
| <math>\text{the following are identical subsets of}~ O \times S \, :</math>
| <math>\text{the following are identical subsets of}~ O \, :</math>
|}
|}
|-
|-
|- style="height:40px"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{D10a.}</math>
| width="18%" style="border-top:1px solid black" | <math>\operatorname{D12a.}</math>
| width="80%" style="border-top:1px solid black" | <math>L_{OS}\!</math>
| width="80%" style="border-top:1px solid black" | <math>L_{OS} \cdot x</math>
|- style="height:40px"
|
| <math>\operatorname{D12b.}</math>
| <math>\operatorname{Den}^L \cdot x</math>
|- style="height:40px"
|
| <math>\operatorname{D12c.}</math>
| <math>\operatorname{Den}^L |_x</math>
|- style="height:40px"
|
| <math>\operatorname{D12d.}</math>
| <math>\operatorname{Den}^L (-, x)</math>
|- style="height:40px"
|- style="height:40px"
|
|
| <math>\operatorname{D10b.}</math>
| <math>\operatorname{D12e.}</math>
| <math>\operatorname{Den}^L</math>
| <math>\operatorname{Den}(L, x)</math>
|- style="height:40px"
|- style="height:40px"
|
|
| <math>\operatorname{D10c.}</math>
| <math>\operatorname{D12f.}</math>
| <math>\operatorname{Den}(L)</math>
| <math>\operatorname{Den}(L) \cdot x</math>
|- style="height:40px"
|- style="height:40px"
|
|
| <math>\operatorname{D10d.}</math>
| <math>\operatorname{D12g.}</math>
| <math>\operatorname{proj}_{OS}(L)</math>
| <math>\{ o \in O ~:~ (o, x) \in \operatorname{Den}(L) \}</math>
|- style="height:40px"
|- style="height:40px"
|
|
| <math>\operatorname{D10e.}</math>
| <math>\operatorname{D12h.}</math>
| <math>\{ (o, s) \in O \times S ~:~ (o, s, i) \in L ~\operatorname{for~some}~ i \in I \}</math>
| <math>\{ o \in O ~:~ (o, x, i) \in L ~\operatorname{for~some}~ i \in I \}</math>
|}
|}
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