MyWikiBiz, Author Your Legacy — Wednesday November 05, 2025
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, 05:04, 10 February 2009
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| | ===Definition 13=== | | ===Definition 13=== |
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| − | <pre>
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| − | Definition 13
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| − | If R c OxSxI,
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| − | then the following are identical subsets of SxI:
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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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| − | D13d. {<x,y> C SxI : Den(R, x) = Den(R, y)}
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| − | </pre>
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| | <br> | | <br> |
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| | |- style="height:40px; text-align:center" | | |- style="height:40px; text-align:center" |
| | | width="80%" | | | | width="80%" | |
| − | | width="20%" | <math>\operatorname{Definition~8}</math> | + | | width="20%" | <math>\operatorname{Definition~13}</math> |
| | |} | | |} |
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| | |- 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{D8a.}</math> | + | | width="18%" style="border-top:1px solid black" | <math>\operatorname{D13a.}</math> |
| − | | width="80%" style="border-top:1px solid black" | <math>L_{SI}\!</math> | + | | width="80%" style="border-top:1px solid black" | <math>\operatorname{Der}^L</math> |
| − | |- style="height:40px"
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| − | | <math>\operatorname{D8b.}</math>
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| − | | <math>\operatorname{Con}^L</math> | |
| | |- style="height:40px" | | |- style="height:40px" |
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| − | | <math>\operatorname{D8c.}</math> | + | | <math>\operatorname{D13b.}</math> |
| − | | <math>\operatorname{Con}(L)</math> | + | | <math>\operatorname{Der}(L)</math> |
| | |- style="height:40px" | | |- style="height:40px" |
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| − | | <math>\operatorname{D8d.}</math> | + | | <math>\operatorname{D13c.}</math> |
| − | | <math>\operatorname{proj}_{SI}(L)</math> | + | | <math>\{ (x, y) \in S \times I ~:~ \operatorname{Den}^L|_x = \operatorname{Den}^L|_y \}</math> |
| | |- style="height:40px" | | |- style="height:40px" |
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| − | | <math>\operatorname{D8e.}</math> | + | | <math>\operatorname{D13d.}</math> |
| − | | <math>\{ (s, i) \in S \times I ~:~ (o, s, i) \in L ~\operatorname{for~some}~ o \in O \}</math> | + | | <math>\{ (x, y) \in S \times I ~:~ \operatorname{Den}(L, x) = \operatorname{Den}(L, y) \}</math> |
| | |} | | |} |
| | |} | | |} |