yes your right i focussed that point of beeing aware of the statement you can deduce by considering things that never hapen wich is explained unfortunatly in english in the 'see there' above for an other reason of being purely finicaty
i didnt see the IF that is on the definition
but in reality i was used to deal whith that closing or unclosing matter with groups or dual and i doubt (that is my pericularity) that an empty set can be a group or a dual (maybe you don't know the word group) because of the abcence of some neutral elements