definition A.529 Hausdorff; second countable; locally compact

open in the book · appendices/A-long-proofs.tex:25873 · p. 3051

ground object -- no derivation owed

Rests on

depends_on definition 6.9 Compact set ¶
- depends_on definition 6.5 Open cover ¶
  - 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 equation 3.51 eq:set-indexed ¶ ↺
depends_on definition 6.2 Open set ¶ ↺
depends_on definition 6.1 Topological space ¶ ↺

Supports

depends_on lemma A.530 Two elementary facts about compactness ¶
- depends_on proposition A.532 Separation and countability of the quotient ¶
  - depends_on remark A.542 Where each hypothesis is spent ¶
  - depends_on theorem A.537 The smooth structure on the orbit space ¶

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`	→	Compact set	declared	appendices/A-long-proofs.tex:25880
`depends_on`	→	Open set	declared	appendices/A-long-proofs.tex:25880
`depends_on`	→	Topological space	declared	appendices/A-long-proofs.tex:25880
`depends_on`	←	Two elementary facts about compactness	declared	appendices/A-long-proofs.tex:25904