definition 13.108 Star-shaped domain

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5161 · p. 516

ground object -- no derivation owed

Rests on

depends_on definition 6.2 Open set ¶
- depends_on definition 6.1 Topological space ¶
  - depends_on definition 3.31 Empty set ¶
  - depends_on definition 3.35 Union, intersection, difference ¶
    - depends_on definition 3.8 Conjunction ¶
    - depends_on definition 3.9 Disjunction ¶
    - depends_on definition 3.7 Negation ¶
  - depends_on definition 3.30 Subset ¶
  - depends_on equation 3.51 eq:set-indexed ¶
depends_on equation 6.12 eq:top-euclidean-metric ¶

Supports

depends_on theorem 13.109 Converse of the Poincaré lemma on a star-shaped domain ¶
- depends_on example 13.110 Closed but not exact: the angle form ¶
- depends_on theorem 13.112 Symmetric analogue of the converse Poincaré lemma ¶

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`	→	Open set	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5166
`depends_on`	→	eq:top-euclidean-metric	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5166
`depends_on`	←	Converse of the Poincaré lemma on a star-shaped domain	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5181