omega-Compact Space
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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 Lindelöf. 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 Lindelöf but not -compact. In fact, the countable complement topology is Lindelöf but neither -compact nor locally compact.

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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 Lindelöf. 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 Lindelöf but not -compact. In fact, the countable complement topology is Lindelöf but neither -compact nor locally compact.