Definition of a topology on a set $X$: may $I$ contain uncountable many elements or is it restricted to be finite or countable?

Question

I've the following definition of a topology $\mathcal I$ on a set $X$:

(T1) $U_a \in \mathcal I, a \in I \Rightarrow \cup_{a \in I} U_a \in \mathcal I$

(T2) $U_1, U_2 \in \mathcal I \Rightarrow U_1 \cap U_2 \in \mathcal I$

(T3) $\emptyset, X \in \mathcal I$

Now nothing is stated about $I$. I guess it is an index set or a general set ? May $I$ contain uncountable many elements or is it restricted to be finite or countable ?