Compactness

• A Simple Example of a Lindelöf Space
  The real line is a simple Lindelöf space: its countable rational-interval basis lets you extract a countable subcover from any open cover.
• Is Every Subset of a Compact Set Compact?
  A subset of a compact space is not necessarily compact. Closed subsets are compact, and in compact Hausdorff spaces, compact subsets are exactly the closed subsets.