Editing Topological property (section)

=== Countability conditions ===
{{See also|Axiom of countability}}
* '''Separable'''. A space is [[separable (topology)|separable]] if it has a [[countable]] dense subset.
* '''First-countable'''. A space is [[first-countable space|first-countable]] if every point has a [[countable]] local base.
* '''Second-countable'''. A space is [[second-countable space|second-countable]] if it has a [[countable]] base for its topology. Second-countable spaces are always separable, first-countable and Lindelöf.
* '''Lindelöf'''. A space is [[first-countable space|Lindelöf]] if every open cover has a [[countable]] subcover.
* '''''σ''-compact'''. A space is [[second-countable space|σ-compact]] if it is the union of [[Countable set|countably]] many [[Compact space|compact]] [[Subspace topology|subspaces]].