lemma A.367 Homotopy lifting

open in the book · appendices/A-long-proofs.tex:17538 · p. 2966

Rests on

depends_on lemma A.365 Lebesgue number ¶
- 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 theorem 6.11 Heine–Borel on $\R$ ¶
  - depends_on axiom 7.1 Completeness of $\R$ ¶
  - depends_on definition 6.9 Compact set ¶
    - depends_on definition 6.5 Open cover ¶
      - depends_on definition 6.2 Open set ¶ ↺
      - depends_on equation 3.51 eq:set-indexed ¶ ↺
  - proves proof ch:04-topology@proof-2 ¶
- proves proof app:A-long-proofs@proof-218 ¶
depends_on lemma A.366 Unique path lifting ¶
- depends_on definition A.361 Covering map ¶
  - depends_on definition 6.6 Continuous map ¶
    - depends_on definition 3.53 Preimage ¶
    - depends_on definition 6.2 Open set ¶ ↺
    - depends_on definition 6.1 Topological space ¶ ↺
  - depends_on definition 6.2 Open set ¶ ↺
- depends_on lemma A.365 Lebesgue number ¶ ↺
- proves proof app:A-long-proofs@proof-219 ¶
proves proof app:A-long-proofs@proof-220 ¶

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Edges

type	direction	node	provenance	where
`depends_on`	→	Lebesgue number	declared	appendices/A-long-proofs.tex:17548
`depends_on`	→	Unique path lifting	declared	appendices/A-long-proofs.tex:17548
`proves`	←	app:A-long-proofs@proof-220	declared	appendices/A-long-proofs.tex:17551