Disjoint Union (topology) - Preservation of Topological Properties

Preservation of Topological Properties

  • every disjoint union of discrete spaces is discrete
  • Separation
    • every disjoint union of T0 spaces is T0
    • every disjoint union of T1 spaces is T1
    • every disjoint union of Hausdorff spaces is Hausdorff
  • Connectedness
    • the disjoint union of two or more nonempty topological spaces is disconnected

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