theorem 6.12 Heine–Borel in $\R^{N}$

open in the book · parts/02-mathematical-methods/04-topology.tex:163 · p. 195

Rests on

depends_on axiom 7.1 Completeness of $\R$ ¶
depends_on definition 6.3 Closed 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 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 6.9 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-3 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Completeness of $\R$	declared	parts/02-mathematical-methods/04-topology.tex:166
`depends_on`	→	Closed set	declared	parts/02-mathematical-methods/04-topology.tex:166
`depends_on`	→	Compact set	declared	parts/02-mathematical-methods/04-topology.tex:166
`proves`	←	ch:04-topology@proof-3	declared	parts/02-mathematical-methods/04-topology.tex:169