\(
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Math and science::Topology
Compactness. Subspaces
How do compactness and subspaces interact?
- A subspace of a compact space [is compact/is not necessarily compact?].
- Every closed subspace of a compact space [is compact/is not necessarily compact?].
- Every compact subspace of a compact space [is closed/is not necessarily closed?].
- Every compact subspace of a Hausdorff space [is closed/is not necessarily closed?].
- A subspace of a compact Hausdorff space is [ something iff something].
