Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
topological space property
|
| gptkbp:defines |
A topological space that is the union of countably many compact subsets.
|
| gptkbp:example |
Every countable discrete space is σ-compact.
The long line is not σ-compact. The real line ℝ is σ-compact. |
| https://www.w3.org/2000/01/rdf-schema#label |
σ-compact space
|
| gptkbp:property |
Every compact space is σ-compact.
Every σ-compact space is Lindelöf. A closed subspace of a σ-compact space is σ-compact. A countable union of σ-compact spaces is σ-compact. Every second-countable locally compact Hausdorff space is σ-compact. A continuous image of a σ-compact space is σ-compact. |
| gptkbp:relatedTo |
gptkb:Lindelöf_space
compact space locally compact space |
| gptkbp:bfsParent |
gptkb:Lindelöf_space
|
| gptkbp:bfsLayer |
6
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