Question about how to use Map as a global variable

$(document).ready(function() {
    // Map Common
    Map = function(){
      this.map = new Object();
    };   
    Map.prototype = {   
        put : function(key, value){   
            this.map[key] = value;
        },   
        get : function(key){   
            return this.map[key];
        },
        containsKey : function(key){    
         return key in this.map;
        },
        containsValue : function(value){    
         for(var prop in this.map){
          if(this.map[prop] == value) return true;
         }
         return false;
        },
        isEmpty : function(key){    
         return (this.size() == 0);
        },
        clear : function(){   
         for(var prop in this.map){
          delete this.map[prop];
         }
        },
        remove : function(key){    
         delete this.map[key];
        },
        keys : function(){   
            var keys = new Array();   
            for(var prop in this.map){   
                keys.push(prop);
            }   
            return keys;
        },
        values : function(){   
         var values = new Array();   
            for(var prop in this.map){   
             values.push(this.map[prop]);
            }   
            return values;
        },
        size : function(){
          var count = 0;
          for (var prop in this.map) {
            count++;
          }
          return count;
        }
//        ,
//        //        toStrong:function(){bar s=[];
//          //          for(var prop in this.map) s.push(prop+':'+this.map[prop]);
//          //          return s.join(',');
//        }
    };

    $('#pageTab').on('click', ' li a .close', function() {
      var tabId = $(this).parents('li').children('a').attr('href');
      $(this).parents('li').remove('li');
//      //      titleMap.remove(tabId);
      $(tabId).remove();
      reNumberPages();
      $('#pageTab a:first').tab('show');
    });

    $("#pageTab").on("click", "a", function(e) {
      e.preventDefault();
      $(this).tab('show');
    });
  });

  var pageNum = 1;
  var titleMap = new Map();
  titleMap.put("key","data");
        console.log(titleMap);

  function reNumberPages(){
    pageNum = 1;
    var tabCount = $('#pageTab > li').length;
    $('#pageTab > li').each(function(){
      var pageId = $(this).children('a').attr('href');
      if(pageId == "#page1"){
        return true;
      }
      pageNum++;
      //tab header Title
      $(this).children('a').html(titleMap.get(pageId)+'<button class="close" type="button" ' + 'title="Remove this page">x</button>');
    })
  }


  function addTab(title){
    pageNum++;
    var pageId = '#page'+pageNum;
    titleMap.put(pageId, title);
//    //    titleMap.put(pageId,title);
    // // tab header title
    $('#pageTab').append($('<li><a href="#page' + pageNum + '">' + title +'<button class="close" type="button" ' +'title="Remove this page">x</button>' +'</a></li>'));
    $('#pageTabContent').append($('<div class="tab-pane" id="page' + pageNum +'">Content page' + pageNum + '</div>'));
    $('#page' + pageNum).tab('show');
  }