High Quality Content by WIKIPEDIA articles! In mathematics, a topological space is said to be ?-compact if it is the union of countably many compact subspaces. A space is said to be ?-locally compact if it is both ?-compact and locally compact. Every compact space is ?-compact, and every ?-compact space is Lindelof. The reverse implications do not hold, for example, standard Euclidean space is ?-compact but not compact, and the lower limit topology on the real line is Lindelof but not ?-compact. In fact, the countable complement topology is Lindelof but neither ?-compact nor locally compact.

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