What does $mathbb{R}^E_{gt 0}$ stand for?












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I was studying an article where I encountered $mathbb{R}^E_{gt 0}$. I couldn't find out what does this notation mean exactly.
I'm sorry if my question is basic, I searched this community but I didn't find the answer to my question.



Here is a part of that article:




Given an undirected graph $G=(V, E)$ with positive edge lengths $linmathbb{R}^E_{gt 0}$ on which one desires to compute the shortest path from a vertex $s$ to $t$, ...







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    1












    $begingroup$


    I was studying an article where I encountered $mathbb{R}^E_{gt 0}$. I couldn't find out what does this notation mean exactly.
    I'm sorry if my question is basic, I searched this community but I didn't find the answer to my question.



    Here is a part of that article:




    Given an undirected graph $G=(V, E)$ with positive edge lengths $linmathbb{R}^E_{gt 0}$ on which one desires to compute the shortest path from a vertex $s$ to $t$, ...







    notation







    share|cite|improve this question









    $endgroup$















      1












      1








      1


      1



      $begingroup$


      I was studying an article where I encountered $mathbb{R}^E_{gt 0}$. I couldn't find out what does this notation mean exactly.
      I'm sorry if my question is basic, I searched this community but I didn't find the answer to my question.



      Here is a part of that article:




      Given an undirected graph $G=(V, E)$ with positive edge lengths $linmathbb{R}^E_{gt 0}$ on which one desires to compute the shortest path from a vertex $s$ to $t$, ...







      notation







      share|cite|improve this question









      $endgroup$




      I was studying an article where I encountered $mathbb{R}^E_{gt 0}$. I couldn't find out what does this notation mean exactly.
      I'm sorry if my question is basic, I searched this community but I didn't find the answer to my question.



      Here is a part of that article:




      Given an undirected graph $G=(V, E)$ with positive edge lengths $linmathbb{R}^E_{gt 0}$ on which one desires to compute the shortest path from a vertex $s$ to $t$, ...







      notation




      notation






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      asked Dec 4 '18 at 20:16









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          3 Answers
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          $begingroup$

          The short answer: This is just a terse way of saying that the length $l(e)$ of each edge $e$ is a nonnegative real number i.e., $l(e) in mathbb{R}_{ge 0}$. If you are satisfied with this then you can stop reading here.



          A longer answer: Note that, in general, a function $f: A mapsto B$ can be thought of as a vector $f in B^A$, where for each $a in A$, the $a$-th coordinate of $f$ is $f(a)$, which is in $B$.



          Here $l$ can be thought of as a function $l: E mapsto mathbb{R}_{geq 0}$ and thus a vector in $mathbb{R}^E_{ge 0}$, where for each $e in E$, the $e$-th coordinate of $l$ is $l(e)$, which is in $mathbb{R}_{ge 0}$.






          share|cite|improve this answer











          $endgroup$





















            2












            $begingroup$

            $X^Y$ is the usual notation for the set of functions $Yto X$. With $X=mathbb{R}_{>0}$ the positive reals and $Y=E$ the edges, $linmathbb{R}_{>0}^E$ is just a function associating to each edge $ein E$ a positive real number $l(e)$, its length.






            share|cite|improve this answer









            $endgroup$





















              2












              $begingroup$

              The notation $Bbb R_{>0}^E$ usually means the set of functions from $E$ to $Bbb R_{>0}$, and $Bbb R_{>0}:=(0,infty)$.



              However in the cited text it is not so clear what it means. If the edges are numbered then it is possible to interpret $EsubsetBbb N$, and then $linBbb R_{>0}^E$ is a function that assign to each $kin E$ it length $l(k)in (0,infty)$.



              Where this text comes? Can you give a link to the article?






              share|cite|improve this answer









              $endgroup$













              • $begingroup$
                Here is the link to the article ;)
                $endgroup$
                – 01000110
                Dec 4 '18 at 20:36











              Your Answer





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              3 Answers
              3






              active

              oldest

              votes








              3 Answers
              3






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              2












              $begingroup$

              The short answer: This is just a terse way of saying that the length $l(e)$ of each edge $e$ is a nonnegative real number i.e., $l(e) in mathbb{R}_{ge 0}$. If you are satisfied with this then you can stop reading here.



              A longer answer: Note that, in general, a function $f: A mapsto B$ can be thought of as a vector $f in B^A$, where for each $a in A$, the $a$-th coordinate of $f$ is $f(a)$, which is in $B$.



              Here $l$ can be thought of as a function $l: E mapsto mathbb{R}_{geq 0}$ and thus a vector in $mathbb{R}^E_{ge 0}$, where for each $e in E$, the $e$-th coordinate of $l$ is $l(e)$, which is in $mathbb{R}_{ge 0}$.






              share|cite|improve this answer











              $endgroup$


















                2












                $begingroup$

                The short answer: This is just a terse way of saying that the length $l(e)$ of each edge $e$ is a nonnegative real number i.e., $l(e) in mathbb{R}_{ge 0}$. If you are satisfied with this then you can stop reading here.



                A longer answer: Note that, in general, a function $f: A mapsto B$ can be thought of as a vector $f in B^A$, where for each $a in A$, the $a$-th coordinate of $f$ is $f(a)$, which is in $B$.



                Here $l$ can be thought of as a function $l: E mapsto mathbb{R}_{geq 0}$ and thus a vector in $mathbb{R}^E_{ge 0}$, where for each $e in E$, the $e$-th coordinate of $l$ is $l(e)$, which is in $mathbb{R}_{ge 0}$.






                share|cite|improve this answer











                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  The short answer: This is just a terse way of saying that the length $l(e)$ of each edge $e$ is a nonnegative real number i.e., $l(e) in mathbb{R}_{ge 0}$. If you are satisfied with this then you can stop reading here.



                  A longer answer: Note that, in general, a function $f: A mapsto B$ can be thought of as a vector $f in B^A$, where for each $a in A$, the $a$-th coordinate of $f$ is $f(a)$, which is in $B$.



                  Here $l$ can be thought of as a function $l: E mapsto mathbb{R}_{geq 0}$ and thus a vector in $mathbb{R}^E_{ge 0}$, where for each $e in E$, the $e$-th coordinate of $l$ is $l(e)$, which is in $mathbb{R}_{ge 0}$.






                  share|cite|improve this answer











                  $endgroup$



                  The short answer: This is just a terse way of saying that the length $l(e)$ of each edge $e$ is a nonnegative real number i.e., $l(e) in mathbb{R}_{ge 0}$. If you are satisfied with this then you can stop reading here.



                  A longer answer: Note that, in general, a function $f: A mapsto B$ can be thought of as a vector $f in B^A$, where for each $a in A$, the $a$-th coordinate of $f$ is $f(a)$, which is in $B$.



                  Here $l$ can be thought of as a function $l: E mapsto mathbb{R}_{geq 0}$ and thus a vector in $mathbb{R}^E_{ge 0}$, where for each $e in E$, the $e$-th coordinate of $l$ is $l(e)$, which is in $mathbb{R}_{ge 0}$.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Dec 4 '18 at 22:04

























                  answered Dec 4 '18 at 20:22









                  MikeMike

                  3,507411




                  3,507411























                      2












                      $begingroup$

                      $X^Y$ is the usual notation for the set of functions $Yto X$. With $X=mathbb{R}_{>0}$ the positive reals and $Y=E$ the edges, $linmathbb{R}_{>0}^E$ is just a function associating to each edge $ein E$ a positive real number $l(e)$, its length.






                      share|cite|improve this answer









                      $endgroup$


















                        2












                        $begingroup$

                        $X^Y$ is the usual notation for the set of functions $Yto X$. With $X=mathbb{R}_{>0}$ the positive reals and $Y=E$ the edges, $linmathbb{R}_{>0}^E$ is just a function associating to each edge $ein E$ a positive real number $l(e)$, its length.






                        share|cite|improve this answer









                        $endgroup$
















                          2












                          2








                          2





                          $begingroup$

                          $X^Y$ is the usual notation for the set of functions $Yto X$. With $X=mathbb{R}_{>0}$ the positive reals and $Y=E$ the edges, $linmathbb{R}_{>0}^E$ is just a function associating to each edge $ein E$ a positive real number $l(e)$, its length.






                          share|cite|improve this answer









                          $endgroup$



                          $X^Y$ is the usual notation for the set of functions $Yto X$. With $X=mathbb{R}_{>0}$ the positive reals and $Y=E$ the edges, $linmathbb{R}_{>0}^E$ is just a function associating to each edge $ein E$ a positive real number $l(e)$, its length.







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered Dec 4 '18 at 20:21









                          user10354138user10354138

                          7,3772925




                          7,3772925























                              2












                              $begingroup$

                              The notation $Bbb R_{>0}^E$ usually means the set of functions from $E$ to $Bbb R_{>0}$, and $Bbb R_{>0}:=(0,infty)$.



                              However in the cited text it is not so clear what it means. If the edges are numbered then it is possible to interpret $EsubsetBbb N$, and then $linBbb R_{>0}^E$ is a function that assign to each $kin E$ it length $l(k)in (0,infty)$.



                              Where this text comes? Can you give a link to the article?






                              share|cite|improve this answer









                              $endgroup$













                              • $begingroup$
                                Here is the link to the article ;)
                                $endgroup$
                                – 01000110
                                Dec 4 '18 at 20:36
















                              2












                              $begingroup$

                              The notation $Bbb R_{>0}^E$ usually means the set of functions from $E$ to $Bbb R_{>0}$, and $Bbb R_{>0}:=(0,infty)$.



                              However in the cited text it is not so clear what it means. If the edges are numbered then it is possible to interpret $EsubsetBbb N$, and then $linBbb R_{>0}^E$ is a function that assign to each $kin E$ it length $l(k)in (0,infty)$.



                              Where this text comes? Can you give a link to the article?






                              share|cite|improve this answer









                              $endgroup$













                              • $begingroup$
                                Here is the link to the article ;)
                                $endgroup$
                                – 01000110
                                Dec 4 '18 at 20:36














                              2












                              2








                              2





                              $begingroup$

                              The notation $Bbb R_{>0}^E$ usually means the set of functions from $E$ to $Bbb R_{>0}$, and $Bbb R_{>0}:=(0,infty)$.



                              However in the cited text it is not so clear what it means. If the edges are numbered then it is possible to interpret $EsubsetBbb N$, and then $linBbb R_{>0}^E$ is a function that assign to each $kin E$ it length $l(k)in (0,infty)$.



                              Where this text comes? Can you give a link to the article?






                              share|cite|improve this answer









                              $endgroup$



                              The notation $Bbb R_{>0}^E$ usually means the set of functions from $E$ to $Bbb R_{>0}$, and $Bbb R_{>0}:=(0,infty)$.



                              However in the cited text it is not so clear what it means. If the edges are numbered then it is possible to interpret $EsubsetBbb N$, and then $linBbb R_{>0}^E$ is a function that assign to each $kin E$ it length $l(k)in (0,infty)$.



                              Where this text comes? Can you give a link to the article?







                              share|cite|improve this answer












                              share|cite|improve this answer



                              share|cite|improve this answer










                              answered Dec 4 '18 at 20:21









                              MasacrosoMasacroso

                              13k41746




                              13k41746












                              • $begingroup$
                                Here is the link to the article ;)
                                $endgroup$
                                – 01000110
                                Dec 4 '18 at 20:36


















                              • $begingroup$
                                Here is the link to the article ;)
                                $endgroup$
                                – 01000110
                                Dec 4 '18 at 20:36
















                              $begingroup$
                              Here is the link to the article ;)
                              $endgroup$
                              – 01000110
                              Dec 4 '18 at 20:36




                              $begingroup$
                              Here is the link to the article ;)
                              $endgroup$
                              – 01000110
                              Dec 4 '18 at 20:36


















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