Question

prove that the intersection of a finite collection of open set is open​

Answer 1

Answer:

the intersection of any finite collection of open subsets of X is open. Proof. (1) The whole space is open because it contains all open balls, and the empty set is open because it does not contain any points. ... Since this set is open, it contains an open ball about x; clearly, this ball lies in A.

Answer 2

Answer:

the intersection of any finite collection of open subsets of X is open. Proof. (1) The whole space is open because it contains all open balls, and the empty set is open because it does not contain any points. ... Since this set is open, it contains an open ball about x; clearly, this ball lies in A.