definition A.361 Covering map

open in the book · appendices/A-long-proofs.tex:17375 · p. 2964

ground object -- no derivation owed

Rests on

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 3.8 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 definition 6.1 Topological space ¶ ↺
depends_on definition 6.2 Open set ¶ ↺

Supports

depends_on lemma A.366 Unique path lifting ¶
- depends_on lemma A.367 Homotopy lifting ¶
depends_on lemma A.369 $\Phi$ is a two-sheeted covering ¶
depends_on theorem A.364 Covering homomorphisms ¶
depends_on theorem A.363 Monodromy ¶
- depends_on theorem A.364 Covering homomorphisms ¶ ↺

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`	→	Continuous map	declared	appendices/A-long-proofs.tex:17384
`depends_on`	→	Open set	declared	appendices/A-long-proofs.tex:17384
`depends_on`	←	Unique path lifting	declared	appendices/A-long-proofs.tex:17489
`depends_on`	←	$\Phi$ is a two-sheeted covering	declared	appendices/A-long-proofs.tex:17757
`depends_on`	←	Covering homomorphisms	declared	appendices/A-long-proofs.tex:17439
`depends_on`	←	Monodromy	declared	appendices/A-long-proofs.tex:17421