Error: TypeError: $(…).dialog is not a function

Be sure to insert full version of jQuery UI. Also you should init the dialog first:

$(function () {
  $( "#dialog1" ).dialog({
    autoOpen: false
  });
  
  $("#opener").click(function() {
    $("#dialog1").dialog('open');
  });
});

<script src="https://code.jquery.com/jquery-1.11.1.min.js"></script>
 
<script src="https://code.jquery.com/ui/1.11.1/jquery-ui.min.js"></script>

<link rel="stylesheet" href="https://code.jquery.com/ui/1.11.1/themes/smoothness/jquery-ui.css" />

<button id="opener">open the dialog</button>
<div id="dialog1" title="Dialog Title" hidden="hidden">I'm a dialog</div>