lemma A.366 Unique path lifting

open in the book · appendices/A-long-proofs.tex:17483 · p. 2966

Rests on

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 3.31 Empty set ¶
      - depends_on definition 3.35 Union, intersection, difference ¶
      - depends_on definition 3.30 Subset ¶
      - depends_on equation 3.51 eq:set-indexed ¶
  - depends_on definition 6.1 Topological space ¶ ↺
- depends_on definition 6.2 Open set ¶ ↺
depends_on lemma A.365 Lebesgue number ¶
- depends_on definition 6.2 Open set ¶ ↺
- 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 ¶
proves proof app:A-long-proofs@proof-219 ¶

Supports

depends_on lemma A.367 Homotopy lifting ¶

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`	→	Covering map	declared	appendices/A-long-proofs.tex:17489
`depends_on`	→	Lebesgue number	declared	appendices/A-long-proofs.tex:17489
`depends_on`	←	Homotopy lifting	declared	appendices/A-long-proofs.tex:17548
`proves`	←	app:A-long-proofs@proof-219	declared	appendices/A-long-proofs.tex:17492