In French mathematics, what is the difference between saying "l'ensemble est fermé" and "l'ensemble est clos"?
The usual word is fermé in topology (« un fermé est le complémentaire d'un ouvert » = “a closed set is the complement of an open set”), and clos for closure under operations (« corps algébriquement clos » = “algebraically closed field”; “clôture algébrique” = “algebraic closure”).
While there is a connection between the two concepts — a closed set in topology is closed under the operation “taking a limit”¹ — the two adjectives are not interchangeable. There are even cases where the two words have different meaning: the fermeture algébrique of a subfield K in a field L is the set of elements of the field L that are algebraic over the subfield L, whereas the clôture algébrique of K is an algebraically closed superfield, which is different if L is not algebraically closed.
¹ Restrictions apply. Consult a mathematics text for details.