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Revision as of 16:14, 9 February 2009
, 16:14, 9 February 2009→Definition 11
===Definition 11===
===Definition 11===
<br>
<br>
|- style="height:40px; text-align:center"
|- style="height:40px; text-align:center"
| width="80%" |
| width="80%" |
| width="20%" | <math>\operatorname{Definition~9}</math>
| width="20%" | <math>\operatorname{Definition~11}</math>
|}
|}
|-
|-
|
|
| <math>\text{then}\!</math>
| <math>\text{then}\!</math>
| <math>\text{the following are identical subsets of}~ I \times S \, :</math>
| <math>\text{the following are identical subsets of}~ S \times O \, :</math>
|}
|}
|-
|-
|- style="height:50px"
|- style="height:50px"
| 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{D9a.}</math>
| width="18%" style="border-top:1px solid black" | <math>\operatorname{D11a.}</math>
| width="80%" style="border-top:1px solid black" | <math>L_{IS}\!</math>
| width="80%" style="border-top:1px solid black" | <math>L_{SO}\!</math>
|- style="height:50px"
|- style="height:50px"
|
|
| <math>\operatorname{D9b.}</math>
| <math>\operatorname{D11b.}</math>
| <math>\overset{\smile}{L_{SI}}</math>
| <math>\overset{\smile}{L_{OS}}</math>
|- style="height:50px"
|- style="height:50px"
|
|
| <math>\operatorname{D9c.}</math>
| <math>\operatorname{D11c.}</math>
| <math>\overset{\smile}{\operatorname{Con}^L}</math>
| <math>\overset{\smile}{\operatorname{Den}^L}</math>
|- style="height:50px"
|- style="height:50px"
|
|
| <math>\operatorname{D9d.}</math>
| <math>\operatorname{D11d.}</math>
| <math>\overset{\smile}{\operatorname{Con}(L)}</math>
| <math>\overset{\smile}{\operatorname{Den}(L)}</math>
|- style="height:50px"
|- style="height:50px"
|
|
| <math>\operatorname{D9e.}</math>
| <math>\operatorname{D11e.}</math>
| <math>\operatorname{proj}_{IS}(L)</math>
| <math>\operatorname{proj}_{SO}(L)</math>
|- style="height:50px"
|- style="height:50px"
|
|
| <math>\operatorname{D9f.}</math>
| <math>\operatorname{D11f.}</math>
| <math>\operatorname{Conv}(\operatorname{Con}(L))</math>
| <math>\operatorname{Conv}(\operatorname{Den}(L))</math>
|- style="height:50px"
|- style="height:50px"
|
|
| <math>\operatorname{D9g.}</math>
| <math>\operatorname{D11g.}</math>
| <math>\{ (i, s) \in I \times S ~:~ (o, s, i) \in L ~\operatorname{for~some}~ o \in O \}</math>
| <math>\{ (s, o) \in S \times O ~:~ (o, s, i) \in L ~\operatorname{for~some}~ i \in I \}</math>
|}
|}
|}
|}
