Open Sets confusion

Question

This might be a trivial question, but if we are given some $X$ as an infinite set. Consider the finite complement topology, $\forall x\ne y\in X$, why is the set $U = X-\{y\}$ still open?

Answer 1

The set $U = X\setminus\{y\}$ will be open because its complement, $U^c = \{y\}$, is finite.