Countability Axioms

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Unlike compactness and connectedness, countability and separation are problems that come about as a direct result of the study of Topology itself, such as imbedding a given space in a metric space or in a compact Hausdorff space. Solutions to these problems involve the Countability Axioms, as well as their related counterparts the separation axioms.[1]


  1. First Countability Axiom
  2. Second Countability Axiom

Further Reading

See Also


  1. Munkres, James R. Topology, 2015. pg. 187-189.