I just had a quick question.

If $\displaystyle \mathcal{B}$ is a basis for a topology on a set $\displaystyle X,$ defined in the way

1)$\displaystyle X = \displaystyle\bigcup_{B \in \mathcal{B}} B$

2) If $\displaystyle B_1, B_2 \in \mathcal{B},$ and$\displaystyle x \in B_1 \cap B_2$, then there exists$\displaystyle B_3 \in \mathcal{B}$ such that $\displaystyle x \in B_3 \subseteq B_1 \cap B_2$

Then it is a fact that this generates a topology on $\displaystyle X$, where the sets in the topology are unions of elements of $\displaystyle \mathcal{B}$. But we require $\displaystyle \emptyset$ to be an element in this topology - is it ok to take a union ofnoneof the basis elements?

Thanks for any help.