theorem A.783 Riemann mapping with boundary correspondence, quoted

open in the book · appendices/A-long-proofs.tex:38417 · p. 3180

Rests on

depends_on definition 8.5 Complex derivative ¶
depends_on theorem 8.6 Cauchy–Riemann equations ¶
- 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 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 5.14 Linear independence ¶
- depends_on equation 8.4 eq:cpx-derivative ¶
- proves proof ch:06-complex-analysis@proof-3 ¶

Supports

depends_on corollary A.788 The two parameters are the same parameter ¶
- depends_on theorem A.789 Kirchhoff's contraction coefficient ¶

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`	→	Complex derivative	declared	appendices/A-long-proofs.tex:38426
`depends_on`	→	Cauchy–Riemann equations	declared	appendices/A-long-proofs.tex:38426
`depends_on`	←	The two parameters are the same parameter	declared	appendices/A-long-proofs.tex:38706