Is $W$ a finite-dimensional vector space in Proposition 3.13?












0












$begingroup$


enter image description here




Is $W$ a finite-dimensional vector space in Proposition $3.13$?







manifolds smooth-manifolds







share|cite|improve this question











$endgroup$












  • $begingroup$
    @JackLee It seems there isn't enough information about $W$ in $textbf{ Proposition 3.13}$.
    $endgroup$
    – Born to be proud
    Dec 13 '18 at 12:50










  • $begingroup$
    The tangent space was only defined for finite-dimensional smooth manifolds, so there is no need to explicitely state this.
    $endgroup$
    – TheGeekGreek
    Dec 13 '18 at 14:55


















0












$begingroup$


enter image description here




Is $W$ a finite-dimensional vector space in Proposition $3.13$?







manifolds smooth-manifolds







share|cite|improve this question











$endgroup$












  • $begingroup$
    @JackLee It seems there isn't enough information about $W$ in $textbf{ Proposition 3.13}$.
    $endgroup$
    – Born to be proud
    Dec 13 '18 at 12:50










  • $begingroup$
    The tangent space was only defined for finite-dimensional smooth manifolds, so there is no need to explicitely state this.
    $endgroup$
    – TheGeekGreek
    Dec 13 '18 at 14:55
















0












0








0





$begingroup$


enter image description here




Is $W$ a finite-dimensional vector space in Proposition $3.13$?







manifolds smooth-manifolds







share|cite|improve this question











$endgroup$




enter image description here




Is $W$ a finite-dimensional vector space in Proposition $3.13$?







manifolds smooth-manifolds




manifolds smooth-manifolds






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 13 '18 at 11:31









amWhy

1




1










asked Dec 13 '18 at 11:13









Born to be proudBorn to be proud

825510




825510












  • $begingroup$
    @JackLee It seems there isn't enough information about $W$ in $textbf{ Proposition 3.13}$.
    $endgroup$
    – Born to be proud
    Dec 13 '18 at 12:50










  • $begingroup$
    The tangent space was only defined for finite-dimensional smooth manifolds, so there is no need to explicitely state this.
    $endgroup$
    – TheGeekGreek
    Dec 13 '18 at 14:55




















  • $begingroup$
    @JackLee It seems there isn't enough information about $W$ in $textbf{ Proposition 3.13}$.
    $endgroup$
    – Born to be proud
    Dec 13 '18 at 12:50










  • $begingroup$
    The tangent space was only defined for finite-dimensional smooth manifolds, so there is no need to explicitely state this.
    $endgroup$
    – TheGeekGreek
    Dec 13 '18 at 14:55


















$begingroup$
@JackLee It seems there isn't enough information about $W$ in $textbf{ Proposition 3.13}$.
$endgroup$
– Born to be proud
Dec 13 '18 at 12:50




$begingroup$
@JackLee It seems there isn't enough information about $W$ in $textbf{ Proposition 3.13}$.
$endgroup$
– Born to be proud
Dec 13 '18 at 12:50












$begingroup$
The tangent space was only defined for finite-dimensional smooth manifolds, so there is no need to explicitely state this.
$endgroup$
– TheGeekGreek
Dec 13 '18 at 14:55






$begingroup$
The tangent space was only defined for finite-dimensional smooth manifolds, so there is no need to explicitely state this.
$endgroup$
– TheGeekGreek
Dec 13 '18 at 14:55












2 Answers
2






active

oldest

votes


















1












$begingroup$

The author seems to assume that $W$ is a vector space and also a smooth manifold. So yes, it is finite-dimensional.






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    Yes it is, and there is really no need to write down that explicitly.
    The theorem states that there is a canonical isomorphism $Vcong T_aV$ when $V$ is finite-dimensional, so in writing $Wcong T_{La}W$ it is implicitly assumed that $W$ is finite-dimensional as well as it is using this canonical isomorphism for $W.$






    share|cite|improve this answer









    $endgroup$













      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3037877%2fis-w-a-finite-dimensional-vector-space-in-proposition-3-13%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      1












      $begingroup$

      The author seems to assume that $W$ is a vector space and also a smooth manifold. So yes, it is finite-dimensional.






      share|cite|improve this answer









      $endgroup$


















        1












        $begingroup$

        The author seems to assume that $W$ is a vector space and also a smooth manifold. So yes, it is finite-dimensional.






        share|cite|improve this answer









        $endgroup$
















          1












          1








          1





          $begingroup$

          The author seems to assume that $W$ is a vector space and also a smooth manifold. So yes, it is finite-dimensional.






          share|cite|improve this answer









          $endgroup$



          The author seems to assume that $W$ is a vector space and also a smooth manifold. So yes, it is finite-dimensional.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Dec 13 '18 at 11:25









          ChristophChristoph

          12k1642




          12k1642























              1












              $begingroup$

              Yes it is, and there is really no need to write down that explicitly.
              The theorem states that there is a canonical isomorphism $Vcong T_aV$ when $V$ is finite-dimensional, so in writing $Wcong T_{La}W$ it is implicitly assumed that $W$ is finite-dimensional as well as it is using this canonical isomorphism for $W.$






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                Yes it is, and there is really no need to write down that explicitly.
                The theorem states that there is a canonical isomorphism $Vcong T_aV$ when $V$ is finite-dimensional, so in writing $Wcong T_{La}W$ it is implicitly assumed that $W$ is finite-dimensional as well as it is using this canonical isomorphism for $W.$






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  Yes it is, and there is really no need to write down that explicitly.
                  The theorem states that there is a canonical isomorphism $Vcong T_aV$ when $V$ is finite-dimensional, so in writing $Wcong T_{La}W$ it is implicitly assumed that $W$ is finite-dimensional as well as it is using this canonical isomorphism for $W.$






                  share|cite|improve this answer









                  $endgroup$



                  Yes it is, and there is really no need to write down that explicitly.
                  The theorem states that there is a canonical isomorphism $Vcong T_aV$ when $V$ is finite-dimensional, so in writing $Wcong T_{La}W$ it is implicitly assumed that $W$ is finite-dimensional as well as it is using this canonical isomorphism for $W.$







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Dec 13 '18 at 14:27









                  positrón0802positrón0802

                  4,313520




                  4,313520






























                      draft saved

                      draft discarded




















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3037877%2fis-w-a-finite-dimensional-vector-space-in-proposition-3-13%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      Popular posts from this blog

                      Wiesbaden

                      Image
                      Wappen Deutschlandkarte 50.0825 8.24 117 Koordinaten: 50° 5′  N , 8° 14′  O Basisdaten Bundesland: Hessen Regierungsbezirk: Darmstadt Höhe: 117 m ü. NHN Fläche: 203,93 km 2 Einwohner: 278.654 (31. Dez. 2017) [1] Bevölkerungsdichte: 1366 Einwohner je km 2 Postleitzahlen: 65183–65207, 55246, 55252 Vorlage:Infobox Gemeinde in Deutschland/Wartung/PLZ enthält Text Vorwahlen: 0611, 06122, 06127, 06134 Kfz-Kennzeichen: WI Gemeindeschlüssel: 06 4 14 000 LOCODE: DE WIB NUTS: DE714 Stadtgliederung: 26 Ortsbezirke Adresse der Stadtverwaltung: Schlossplatz 6 65183 Wiesbaden Webpräsenz: www.wiesbaden.de Oberbürgermeister: Sven Gerich (SPD) Lage der Landeshauptstadt Wiesbaden in Hessen und im Regierungsbezirk Darmstadt Offizielles Logo der Landeshauptstadt Wiesbaden Flagge der Landeshauptstadt Wiesbaden Wiesbaden is
                      Read more

                      Marschland

                      Image
                      Kilometerweite Marsch in den Vier- und Marschlanden am Elbdeich Die Wedeler Marschlandschaft in Schleswig-Holstein Der Hadelner Kanal zur Entwässerung der Marsch Die tief gelegene Marsch und ein Entwässerungskanal Das Schöpfwerk Otterndorf im Land Hadeln zur Entwässerung der Medem verfügte damals bereits über die größte Kreiselpumpe Europas. Das Schöpfwerk in Neuhaus für die Aue und des Neuhaus-Bülkauer Kanals Als Marsch(land) (v. niederdt., altsächs. mersc ) – auch Masch , Mersch oder Schwemmland genannt – bezeichnet man eine nacheiszeitlich entstandene geomorphologische Landform im Gebiet der nordwestdeutschen Küsten und Flüsse sowie vergleichbare Landformen weltweit. Inhaltsverzeichnis 1 Landschaft 2 Entstehung 3 Marschböden 4 Nutzung 5 Marschgebiete in Deutschland 6 Siehe auch 7 Literatur 8 Weblinks 9 Einzelnachweise Landschaft | Marschen sind generell flache Landstriche ohne natürliche Erhebungen. Si
                      Read more

                      Dieringhausen

                      Image
                      Dieringhausen Stadt Gummersbach 50.982777777778 7.5316666666667 165 Koordinaten: 50° 58′ 58″  N , 7° 31′ 54″  O Höhe: 165  (160–245)  m Einwohner: 5055  (30. Jun. 2016) Postleitzahl: 51645 Vorwahl: 02261 Lage von Dieringhausen in Gummersbach Im Hohl ca. 1927–1930 Ansicht von Südwesten bei Bünghausen Dieringhausen (im örtlichen Dialekt Dierkesen ) ist ein Ortsteil von Gummersbach im Oberbergischen Kreis, Regierungsbezirk Köln, Nordrhein-Westfalen (Deutschland). Inhaltsverzeichnis 1 Geographie 2 Geschichte 3 Kultur 3.1 Sehenswürdigkeiten 3.2 Regelmäßige Veranstaltungen 4 Infrastruktur und Wirtschaft 4.1 Verkehr 4.1.1 Schienen- und Busverkehr 4.1.2 Straßen 4.2 Öffentliche Einrichtungen 4.2.1 Schulen und Bildungseinrichtungen 4.2.2 Kirchliche Einrichtungen 5 Persönlichkeiten 5.1 In Dieringhausen geboren 5.2 In Dieringhausen gelebt 6 Einzelnachweise 7
                      Read more