A topology is closed under arbitrary union of open sets, and therefore a fortiori also closed under countable union of open sets.
Why do we require arbitrary union rather than just countable union?
What might be an example that would illustrate why we require arbitrary union? Or are they just equivalent when talking about unions of sets?
The most similar question I've found to this one is regarding the validity of arbitrary union without assuming topology as prior.
Edit: This question was not addressed in answers given to a similar seeming post regarding finite intersection, rather than arbitrary or countable intersection.