Definition
A set S in 
is open if for each 
, there exists an open ε-ball around x which is completely contained in S:
open 
, 
Or:
A subset 
is open if its complement is closed.
is both closed and open.
Properties of open set:
(1) The union of any collection of open sets is open.
(2) The intersection of finite many open sets is open.
(3) 
is open if and only if for every 
there exists an r > 0, such that 
(the open ball of radius r around 
) is a subset of S.