lemma A.365 Lebesgue number

open in the book · appendices/A-long-proofs.tex:17459 · p. 2965

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 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 ¶

Supports

depends_on lemma A.367 Homotopy lifting ¶
depends_on lemma A.366 Unique path lifting ¶
- 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`	→	Open set	declared	appendices/A-long-proofs.tex:17463
`depends_on`	→	Heine–Borel on $\R$	declared	appendices/A-long-proofs.tex:17463
`depends_on`	←	Homotopy lifting	declared	appendices/A-long-proofs.tex:17548
`depends_on`	←	Unique path lifting	declared	appendices/A-long-proofs.tex:17489
`proves`	←	app:A-long-proofs@proof-218	declared	appendices/A-long-proofs.tex:17466