| Generalized topologies/Axioms | K0 | K1 | K2 | K3 | K4 | K5 | K6 |
| Smyth space | ٭ | ٭ | ٭ | ||||
| Pre-topology | ٭ | ٭ | ٭ | ٭ | |||
| Pre-topology with every open set is closed | ٭ | ٭ | ٭ | ٭ | ٭ | ||
| Alexandroff topology | ٭ | ٭ | ٭ | ٭ | ٭ | ||
| Clo-open topology | ٭ | ٭ | ٭ | ٭ | ٭ | ٭ | ٭ |