The user here wants to reopen their deleted question because they have significantly lengthened it and included more effort. However, the reopen queue invalidates it and the question requires many MathJax edits.
Basically the title. I have a feeling that this is not a topology and the issue would come up when I consider arbitrary union of countable subsets in T which may not be countable and the complement of this union needn't be countable either. But I am unable to come up with such an example. Kindly ...