Chain selectors are not limited just to classes, you can do it for both classes and ids.
Classes
.classA.classB {
/*style here*/
}
Class & Id
.classA#idB {
/*style here*/
}
Id & Id
#idA#idB {
/*style here*/
}
All good current browsers support this except IE 6, it selects based on the last selector in the list. So ".classA.classB" will select based on just ".classB".
For your case
li.left.ui-class-selector {
/*style here*/
}
or
.left.ui-class-selector {
/*style here*/
}