About: Exhaustion by compact sets

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In mathematics, especially general topology and analysis, an exhaustion by compact sets of a topological space is a nested sequence of compact subsets of (i.e. ), such that is contained in the interior of , i.e. for each and . A space admitting an exhaustion by compact sets is called exhaustible by compact sets. For example, consider and the sequence of closed balls . Occasionally some authors drop the requirement that is in the interior of , but then the property becomes the same as the space being σ-compact, namely a countable union of compact subsets.

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  • In mathematics, especially general topology and analysis, an exhaustion by compact sets of a topological space is a nested sequence of compact subsets of (i.e. ), such that is contained in the interior of , i.e. for each and . A space admitting an exhaustion by compact sets is called exhaustible by compact sets. For example, consider and the sequence of closed balls . Occasionally some authors drop the requirement that is in the interior of , but then the property becomes the same as the space being σ-compact, namely a countable union of compact subsets. (en)
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  • Exhaustion by compact sets (en)
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  • ExhaustionByCompactSets (en)
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  • In mathematics, especially general topology and analysis, an exhaustion by compact sets of a topological space is a nested sequence of compact subsets of (i.e. ), such that is contained in the interior of , i.e. for each and . A space admitting an exhaustion by compact sets is called exhaustible by compact sets. For example, consider and the sequence of closed balls . Occasionally some authors drop the requirement that is in the interior of , but then the property becomes the same as the space being σ-compact, namely a countable union of compact subsets. (en)
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  • Exhaustion by compact sets (en)
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