definition 3.59 Equivalence class

open in the book · parts/02-mathematical-methods/01-logic-sets.tex:1488 · p. 34

Rests on

depends_on definition 4.58 Conjugacy classes ¶
- depends_on definition 4.59 Conjugate subgroups ¶
  - depends_on definition 4.60 Normal subgroup ¶
    - depends_on proposition 4.63 Well-definedness of the coset product ¶
    - depends_on proposition 4.70 Characterization of the direct product ¶
    - depends_on proposition 4.75 The two factors inside the semidirect product ¶
      - depends_on example 4.79 The Poincaré group ¶
      - depends_on proposition 4.77 When a semidirect product is direct ¶
    - depends_on proposition 4.77 When a semidirect product is direct ¶ ↺
    - depends_on theorem 4.64 Quotient group ¶
    - depends_on theorem 4.76 Internal characterization of the semidirect product ¶
depends_on definition 4.62 Cosets ¶
- depends_on proposition 4.63 Well-definedness of the coset product ¶ ↺
depends_on definition 3.61 Quotient space ¶
depends_on theorem 3.60 Equivalence classes partition the set ¶
- depends_on lemma A.10 lem:app-comp-welldefined ¶
  - depends_on lemma A.11 Truth lemma ¶
    - depends_on theorem A.12 Model existence ¶
      - depends_on corollary A.14 Compactness ¶
      - depends_on theorem A.13 Completeness ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Equivalence relation	declared	parts/02-mathematical-methods/01-logic-sets.tex:1497
`depends_on`	←	Conjugacy classes	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2062
`depends_on`	←	Cosets	declared	parts/02-mathematical-methods/02-algebraic-structures.tex:2161
`depends_on`	←	Quotient space	declared	parts/02-mathematical-methods/01-logic-sets.tex:1601
`depends_on`	←	Equivalence classes partition the set	declared	parts/02-mathematical-methods/01-logic-sets.tex:1563