So I am new to topology and I've been trying to understand the concept of a basis and am a bit stuck on this statement: The topology $\big\{\varnothing,\{a\},\{b\},\{a,b\}\big\}$ on the set $\{a,b\}$ has the following bases:
1.$\big\{\varnothing,\{a\},\{b\},\{a,b\}\big\}$
2. $\big\{\{a\},\{b\},\{a,b\}\big\}$
My confusion arises in the 2nd base how can $\big\{\{a\},\{b\},\{a,b\}\big\}$ be a base for the topology since no unions of subsets give $\varnothing$?.
Thanks in advance.
The union of an empty collection is defined to be empty. Hence, the empty set is a union of members of any family of sets.