definition 6.29 Sequential compactness
open in the book ·
parts/02-mathematical-methods/04-topology.tex:579
· p. 200
- ground object -- no derivation owed
Rests on
-
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 3.1 Logical proposition ¶
- depends_on definition 3.38 Ordered pair and Cartesian product ¶
-
depends_on
definition 3.23
Predicate
¶
- depends_on definition 3.28 Set ¶
-
depends_on
definition 3.24
Quantifiers
¶
- depends_on definition 3.38 Ordered pair and Cartesian product ¶ ↺
-
depends_on
definition 3.43
Map
¶
- depends_on definition 6.27 Convergence; Cauchy sequence; completeness ¶
Supports
-
depends_on
lemma 6.30
Lebesgue number
¶
-
depends_on
theorem 6.31
Compactness and sequential compactness
¶
-
depends_on
lemma A.230
Sequential characterisation
¶
-
depends_on
lemma A.232
Attainment
¶
- depends_on lemma A.233 Construction of the system ¶
-
depends_on
lemma A.231
Restriction to an invariant closed subspace
¶
- depends_on lemma A.233 Construction of the system ¶ ↺
- depends_on lemma A.234 The eigenvalues tend to zero, with finite multiplicity ¶
-
depends_on
lemma A.232
Attainment
¶
-
depends_on
lemma A.488
Small chords cut off small arcs
¶
- depends_on theorem A.490 Equicontinuity of the normalised class ¶
-
depends_on
lemma A.230
Sequential characterisation
¶
-
depends_on
theorem 6.31
Compactness and sequential compactness
¶
- depends_on theorem 6.31 Compactness and sequential compactness ¶ ↺
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 |
→ | Metric | declared | parts/02-mathematical-methods/04-topology.tex:584 |
depends_on |
→ | Convergence; Cauchy sequence; completeness | declared | parts/02-mathematical-methods/04-topology.tex:584 |
depends_on |
← | Lebesgue number | declared | parts/02-mathematical-methods/04-topology.tex:592 |
depends_on |
← | Compactness and sequential compactness | declared | parts/02-mathematical-methods/04-topology.tex:616 |