Hello. Is it possible to impose a button to remove this <option> on the <option> from selectbox? and how to do it? 
something like that
Well, in general, you can try to do this. You need to insert something into the <option> (text "delete" or a picture), align it, assign a click handler, and delete this <option> by clicking. But in general, the approach is not correct, because in this case, the browser is in charge of everything, so it’s not clear how it will work and whether it will, let alone be multi-browser.
Source: https://ru.stackoverflow.com/questions/544317/
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select2. - Vasily Barbashev