example 6.18 ex:top-simply-connected

open in the book · parts/02-mathematical-methods/04-topology.tex:286 · p. 196

example -- no derivation owed by its kind

Rests on

depends_on definition 6.17 Simply connected space ¶
- 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 6.15 Path-connected space ¶
  - depends_on definition 6.6 Continuous map ¶ ↺

Supports

depends_on lemma 14.34 The $n$-sphere is simply connected for $n \ge 2$ ¶

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`	→	Simply connected space	declared	parts/02-mathematical-methods/04-topology.tex:295
`depends_on`	←	The $n$-sphere is simply connected for $n \ge 2$	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:1270