#Si l'espace entier est une réunion dénombrable de fermés, l'un au moins de ces fermés contient un ouvert (non vide) (Théorème de Baire iii) ) #Un sous-espace vectoriel strict est forcément d'intérieur vide dans un espace complet (donc dire F(N)⊂E et F(N)≠E est faux car F(N) contient un ouvert, donc par déduction F(N)=E) #Rappel: un ensemble d'intérieur vide ne contient aucun ouvert #Rappel: dans un EVN, tout singleton {x} est fermé
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