proposition 6.28 $\varepsilon$–$\delta$ characterization

open in the book · parts/02-mathematical-methods/04-topology.tex:545 · p. 199

Rests on

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 3.8 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 definition 6.1 Topological space ¶ ↺
depends_on definition 6.26 Open ball; metric topology ¶
- depends_on definition 6.24 Metric ¶
  - depends_on definition 3.43 Map ¶
    - depends_on definition 3.24 Quantifiers ¶
      - depends_on definition 3.23 Predicate ¶
    - depends_on definition 3.28 Set ¶
  - depends_on definition 3.38 Ordered pair and Cartesian product ¶
- depends_on definition 6.2 Open set ¶ ↺
- depends_on definition 6.1 Topological space ¶ ↺
proves proof ch:04-topology@proof-9 ¶

Supports

depends_on proposition 12.36 Boundedness is continuity ¶
- depends_on theorem 12.74 Hellinger–Toeplitz ¶
  - depends_on corollary 12.76 Position and momentum are unbounded, and cannot be everywhere defined ¶

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`	→	Continuous map	declared	parts/02-mathematical-methods/04-topology.tex:554
`depends_on`	→	Open ball; metric topology	declared	parts/02-mathematical-methods/04-topology.tex:554
`depends_on`	←	Boundedness is continuity	declared	parts/02-mathematical-methods/10-hilbert-spaces.tex:902
`proves`	←	ch:04-topology@proof-9	declared	parts/02-mathematical-methods/04-topology.tex:557