definition 6.13 Connected space

open in the book · parts/02-mathematical-methods/04-topology.tex:221 · p. 195

ground object -- no derivation owed

Rests on

depends_on definition 3.36 Disjoint sets ¶
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 ¶

Supports

depends_on proposition 6.16 prop:top-path-implies-connected ¶
depends_on theorem 10.77 Strong maximum principle for harmonic functions ¶
depends_on theorem 6.14 Intervals are connected ¶
- depends_on proposition 6.16 prop:top-path-implies-connected ¶ ↺

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`	→	Disjoint sets	declared	parts/02-mathematical-methods/04-topology.tex:224
`depends_on`	→	Open set	declared	parts/02-mathematical-methods/04-topology.tex:224
`depends_on`	←	prop:top-path-implies-connected	declared	parts/02-mathematical-methods/04-topology.tex:264
`depends_on`	←	Strong maximum principle for harmonic functions	declared	parts/02-mathematical-methods/08-pdes.tex:2101
`depends_on`	←	Intervals are connected	declared	parts/02-mathematical-methods/04-topology.tex:238