Here is the list of posts on places where countability matters in topology, so far:
- On countability
- On countability: the compact completed sequence
- Core-compact+well-filtered T0 = sober locally compact
- The Rasiowa-Sikorski lemma and the Baire property
- Quasi-Polish spaces as rounded ideal completions
- The Sorgenfrey line is not consonant
- First-countable spaces and their Smyth powerdomain