open: function(event, ui) { 
//hide close button.
$(this).parent().children().children('.ui-dialog-titlebar-close').hide();
},

	

Here is another option just using CSS that does not over ride every dialog on the page.

The CSS

.no-close .ui-dialog-titlebar-close {display: none }

The HTML <div class="selector" title="No close button">This is a test without a close button</div>

The Javascript.

$( ".selector" ).dialog({ dialogClass: 'no-close' });