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Math and science::Topology

Compactness. Subspaces

How do compactness and subspaces interact?

  1. A subspace of a compact space [is compact/is not necessarily compact?].
  2. Every closed subspace of a compact space [is compact/is not necessarily compact?].
  3. Every compact subspace of a compact space [is closed/is not necessarily closed?].
  4. Every compact subspace of a Hausdorff space [is closed/is not necessarily closed?].
  5. A subspace of a compact Hausdorff space is [ something iff something].