The Clowder Project

9.3 More Constructions With Relations

• Subsection 9.3.1: The Domain and Range of a Relation
  • Definition 9.3.1.1.1: The Domain and Range of a Relation
• Subsection 9.3.2: Binary Unions of Relations
  • Definition 9.3.2.1.1: Binary Unions of Relations
  • Proposition 9.3.2.1.2: Properties of Binary Unions of Relations
• Subsection 9.3.3: Unions of Families of Relations
  • Definition 9.3.3.1.1: The Union of a Family of Relations
  • Proposition 9.3.3.1.2: Properties of Unions of Families of Relations
• Subsection 9.3.4: Binary Intersections of Relations
  • Definition 9.3.4.1.1: Binary Intersections of Relations
  • Proposition 9.3.4.1.2: Properties of Binary Intersections of Relations
• Subsection 9.3.5: Intersections of Families of Relations
  • Definition 9.3.5.1.1: The Intersection of a Family of Relations
  • Proposition 9.3.5.1.2: Properties of Intersections of Families of Relations
• Subsection 9.3.6: Binary Products of Relations
  • Definition 9.3.6.1.1: Binary Products of Relations
  • Proposition 9.3.6.1.2: Properties of Binary Products of Relations
• Subsection 9.3.7: Products of Families of Relations
  • Definition 9.3.7.1.1: The Product of a Family of Relations
• Subsection 9.3.8: The Collage of a Relation
  • Definition 9.3.8.1.1: The Collage of a Relation
  • Notation 9.3.8.1.2: Notation: $\mathsf{Pos}_{/\Delta ^{1}}\webleft (A,B\webright )$
  • Remark 9.3.8.1.3: Unwinding Notation 9.3.8.1.2
  • Proposition 9.3.8.1.4: Properties of Collages of Relations