You can set up a click and focus handler and reuse the same logic for both.
function setFocus(e) {
e.stopPropagation();
$('div.select-styled.active').each(function() {
$(this).removeClass('active').next('ul.select-options').hide();
});
$(this).toggleClass('active').next('ul.select-options').toggle();
};
$styledSelect.click(setFocus);
$styledSelect.focus(setFocus);
Updated CodePen: http://codepen.io/anon/pen/kcpqd