Answer to mike's question

Firstly, there were several semicolons and parentheses missing. I don't believe they were causing a problem but I have corrected them anyway. My suggested solutions is to use the two-function version of .hover(). In the first function (mouseenter) I have changed the behaviour to always show the tooltip, then in the new second function (mouseleave) the code will hide the tooltip only when a menu option has been selected (if the options menu has already been opened). I have use a data('activemenu') parameter to indicate when the options menu has been opened. I have assumed that was the purpose of your data('activesong') parameter so I have removed those references - but you can easily put them back in if you need them. ----------------------- Answer to https://forum.jquery.com/topic/please-help-to-correct-program-tool-tip#14737000003572162

HTML

<div class="provincia"><!-- start provincia -->
    <span class="tip">Choose city</span>
    <ol>
        <li>                       
            <div class="tipo_provinc">
                <div class="seleccion_provincias"></div>
                <ul class="menu_lis"></ul>
            </div>
        </li> 
    </ol>
</div><!-- end provincia -->

CSS

span.provincia_arrow,
a.provincia_tip{
    display:none;
    position:absolute;    
}
a.provincia_tip{     
    height: 23px;
    text-align:center;
    padding:4px 10px 0 10px;
    width: auto;
    background-color:#000;
    border-radius: 5px;
    border: #F00 solid 2px ;
    margin-left:-95px;
    margin-top:-50px;
    color:#FFF;    
    text-decoration:none;     
}
span.provincia_arrow{
    margin-left:-75px;
    margin-top:-25px;     
}
/* START DIV "SELECT PROVINCE" */
div.provincia {/*div superior*/
    font-family: sans-serif;
    font-size: 15px;
    margin-top: 115px;
    margin-left:155px;
}
div.provincia span.tip {    
    display: inline-block;
    min-width: 128px;
    height: 13px;
    color: #000;
    background-color:  #FFF;
    padding: 3px 0 7px 4px;
    cursor: pointer;
    border:3px solid #CCC;    
}
div.provincia ol {/*div inf of "province"*/
    position: absolute;
    display: none;
    border: 1px solid #333;
    width: 96px;
    overflow: hidden;     
    background-color: #000;
    z-index: 10000;
    margin-left:;
    margin-top: -2px;    
    height:100px;    
    border:1px solid #0CF;  
}
div.provincia ol li a {
    margin-left:15px;
    font-size:16px;
    color: #999;    
}
div.provincia ol li a:hover {
    background-color: #666;
    color: #FFF;        
}
div.provincia ol li:last-child {
    border-bottom: none;
}
/* END DIV "SELECT PROVINCE" */

.seleccion_provincias {
    display:none;      
    
    /*this line is commented just to show functionality*/
}

JavaScript

$(document).ready(function() {    
    
     $('div.provincia')
        .append('<a class="provincia_tip">City</a>','<span class="provincia_arrow">▼</div>');
         
    var $tip_provincia = $("a.provincia_tip,span.provincia_arrow");

    $('span.tip').hover(function() {
        $tip_provincia.show();
        $(this).click(function() {
            $('span.tip').data('activesong', true);
        });
        $(".menu_lis li a").click(function(){ 
            $tip_provincia.hide();
            $('span.tip').data('activesong', false);
        });
    }, function() {
        if (!$(this).data('activesong')) {
            $tip_provincia.hide();
        }
    });
    
    /* cache main list elements so each doc click isn't a DOM search*/
    var $lists = $('div.provincia');
    
    $lists.live('click',function(e) {
        e.stopPropagation();
        $lists.not(this).find('<ol:none>').hide();
        var $tgt = $(e.target);
        $(this).find('ol').slideToggle('fast');
        if ($tgt.is('li a')) {
            $(this).find('span.tip').html($tgt.html());
            var value=$tgt.attr('rel');
            $('#test_select').val( value);
        }
    });
    
    var provs = ['Aires','Catamarca','Chaco','Chubut','Córdoba'];
    $.each(provs,function(i,v) {
        $('.seleccion_provincias')
            .append( '<input type= "radio" name="provincias" value="' + v + '" />' );
        $('.menu_lis')
            .append( '<li><a href="#" rel="' + i + '">' + v + '</a></li>' );
    });
    
    $(document).on('click','.menu_lis li a',function(e) {
        e.preventDefault();
        //hide tooltip
        $('.seleccion_provincias :radio:eq(' + $(this).attr('rel') + ')').attr('checked',true);
    });
});