Changes

User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 16:14, 9 February 2009

224 bytes removed , 16:14, 9 February 2009

→‎Definition 11

Line 3,604: Line 3,604:

===Definition 11===

−

~~<pre>~~

−

~~Definition 11~~

−

~~If R c OxSxI,~~

−

~~then the following are identical subsets of SxO:~~

−

~~D11a. RSO~~

−

~~D11b. ROS^~~

−

~~D11c. DenR^~~

−

~~D11d. Den(R)^~~

−

~~D11e. PrSO(R)~~

−

~~D11f. Conv(Den(R))~~

−

~~D11g. {<s, o> C SxO : <o, s, i> C R for some i C I}~~

−

~~</pre>~~

<br>

Line 3,634: Line 3,612:

|- style="height:40px; text-align:center"

| width="80%" |  

−

| width="20%" | <math>\operatorname{Definition~9}</math>

+

| width="20%" | <math>\operatorname{Definition~11}</math>

|}

|-

Line 3,646: Line 3,624:

|  

| <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>

|}

|-

Line 3,653: Line 3,631:

|- style="height:50px"

| 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"

|  

−

| <math>\operatorname{~~D9b~~.}</math>

+

| <math>\operatorname{D11b.}</math>

−

| <math>\overset{\smile}{L_{SI}}</math>

+

| <math>\overset{\smile}{L_{OS}}</math>

|- 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"

|  

−

| <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"

|  

−

| <math>\operatorname{~~D9e~~.}</math>

+

| <math>\operatorname{D11e.}</math>

−

| <math>\operatorname{proj}_{IS}(L)</math>

+

| <math>\operatorname{proj}_{SO}(L)</math>

|- 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"

|  

−

| <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>

|}

Jon Awbrey

12,080

edits