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- W2322817503 abstract "It is well known (see [3]( 1 )) that no continuum (i.e. compact, connected, Hausdorff space) can be written as a countable disjoint union of its (nonvoid) closed subsets. This result can be generalized in two ways into the setting of locally compact, connected, Hausdorff spaces. Using the one point compactification of a locally compact, connected, Hausdorff space X one can easily show that X cannot be written as a countable disjoint union of compact subsets. If one makes the further assumption that X is locally connected, then one can show that X cannot be written as a countable disjoint union of closed subsets.( 2 )" @default.
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- W2322817503 date "1973-09-01" @default.
- W2322817503 modified "2023-10-01" @default.
- W2322817503 title "Spaces which Cannot be Written as a Countable Disjoint Union of Closed Subsets" @default.
- W2322817503 doi "https://doi.org/10.4153/cmb-1973-069-1" @default.
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