definition A.508 Primitive map

open in the book · appendices/A-long-proofs.tex:24811 · p. 3040

ground object -- no derivation owed

Rests on

depends_on definition 7.98 Functions of class $C^{1}$ ¶
- depends_on definition 7.20 Continuity at a point ¶
  - depends_on definition 7.16 Limit ¶
    - depends_on definition 7.2 Absolute value ¶
    - depends_on definition 7.9 Real function ¶
      - depends_on definition 3.43 Map ¶
  - depends_on equation 7.7 eq:ana-limit-left ¶
  - depends_on equation 7.5 eq:ana-limit-right ¶
- depends_on definition 7.97 Partial derivative; gradient ¶
  - depends_on definition 7.26 Derivative of a function at a point ¶
    - depends_on definition 7.16 Limit ¶ ↺
    - depends_on definition 7.9 Real function ¶ ↺
  - depends_on definition 5.15 Basis ¶
    - depends_on definition 5.12 Subspace generated by a set of vectors ¶
      - depends_on definition 5.5 Linear combination ¶
      - depends_on definition 5.7 Vector subspace ¶
      - proves proof ch:03-linear-algebra-representations@proof-3 ¶
    - depends_on definition 5.14 Linear independence ¶
      - depends_on definition 5.5 Linear combination ¶ ↺
depends_on equation 5.19 eq:lin-leibniz-det ¶

Supports

depends_on lemma A.510 Every diffeomorphism factorises locally ¶
- depends_on proposition A.511 The substitution property is universal ¶
  - depends_on remark A.516 The hypotheses of the global form ¶
  - depends_on theorem A.513 Change of variables ¶
    - depends_on corollary A.514 Degeneracy on a negligible set ¶
    - depends_on remark A.516 The hypotheses of the global form ¶ ↺
depends_on lemma A.509 Primitive maps have the substitution property ¶
- depends_on proposition A.511 The substitution property is universal ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Functions of class $C^{1}$	declared	appendices/A-long-proofs.tex:24823
`depends_on`	→	eq:lin-leibniz-det	declared	appendices/A-long-proofs.tex:24823
`depends_on`	←	Every diffeomorphism factorises locally	declared	appendices/A-long-proofs.tex:24909
`depends_on`	←	Primitive maps have the substitution property	declared	appendices/A-long-proofs.tex:24829