A topology on a non-empty set X is a collection of subsets of X, called open subsets, that satisfies three specific axioms: (1) the empty set and the whole set X are in the collection; (2) the union of any family of sets in the collection is also in the collection; and (3) the intersection of any finite collection of sets in the collection is also in the collection.
Conditions: X is a non-empty set.; The collection consists of subsets of X.; The three listed axioms must all hold.
A topology on a non-empty set X is a collection of subsets of X, called open subsets, that satisfies three specific axioms: (1) the empty set and the whole set X are in the collection; (2) the union of any family of sets in the collection is also in the collection; and (3) the intersection of any finite collection of sets in the collection is also in the collection.
Conditions: X is a non-empty set.; The collection consists of subsets of X.; The three listed axioms must all hold.