lemma 6.22 Nearby loops wind alike

open in the book · parts/02-mathematical-methods/04-topology.tex:392 · p. 198

Rests on

depends_on definition 6.20 Winding number ¶
- depends_on lemma 6.19 Continuous argument along a path ¶
  - depends_on theorem 7.24 Extreme value theorem ¶
    - depends_on axiom 7.1 Completeness of $\R$ ¶
    - depends_on proposition 7.22 Sequential characterization ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.4 Convergence ¶
      - proves proof ch:05-real-analysis@proof-7 ¶
    - depends_on theorem 7.7 Bolzano–Weierstrass ¶
      - depends_on corollary A.45 Archimedean property and density of $\Q$ ¶
      - depends_on corollary A.46 Monotone convergence ¶
      - proves proof ch:05-real-analysis@proof-4 ¶
    - proves proof ch:05-real-analysis@proof-9 ¶
  - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
    - depends_on proposition 7.22 Sequential characterization ¶ ↺
    - depends_on theorem 7.7 Bolzano–Weierstrass ¶ ↺
    - proves proof ch:05-real-analysis@proof-10 ¶
  - depends_on theorem 7.23 Intermediate value theorem ¶
    - depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
    - depends_on definition 7.20 Continuity at a point ¶ ↺
    - proves proof ch:05-real-analysis@proof-8 ¶
  - proves proof ch:04-topology@proof-6 ¶
depends_on lemma 6.19 Continuous argument along a path ¶ ↺
proves proof ch:04-topology@proof-7 ¶

Supports

depends_on proposition 6.23 The punctured plane is not simply connected ¶

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`	→	Winding number	declared	parts/02-mathematical-methods/04-topology.tex:400
`depends_on`	→	Continuous argument along a path	declared	parts/02-mathematical-methods/04-topology.tex:400
`depends_on`	←	The punctured plane is not simply connected	declared	parts/02-mathematical-methods/04-topology.tex:423
`proves`	←	ch:04-topology@proof-7	declared	parts/02-mathematical-methods/04-topology.tex:403