Page "Σ-compact space" Paragraph 2

* Every compact space is σ-compact, and every σ-compact space is Lindelöf ( i. e. every open cover has a countable subcover ).

The reverse implications do not hold, for example, standard Euclidean space ( R < sup > n </ sup >) is σ-compact but not compact, and the lower limit topology on the real line is Lindelöf but not σ-compact.

In fact, the countable complement topology is Lindelöf but neither σ-compact nor locally compact.