proposition 6.10 Continuous images of compact sets
open in the book ·
parts/02-mathematical-methods/04-topology.tex:115
· p. 194
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
definition 6.1
Topological space
¶
- depends_on equation 3.51 eq:set-indexed ¶ ↺
-
depends_on
definition 6.2
Open set
¶
-
depends_on
definition 6.5
Open cover
¶
- depends_on definition 6.6 Continuous map ¶
- proves proof ch:04-topology@proof-1 ¶
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 ¶
-
depends_on
proposition A.532
Separation and countability of the quotient
¶
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 | parts/02-mathematical-methods/04-topology.tex:119 |
depends_on |
→ | Continuous map | declared | parts/02-mathematical-methods/04-topology.tex:119 |
depends_on |
← | Two elementary facts about compactness | declared | appendices/A-long-proofs.tex:25904 |
proves |
← | ch:04-topology@proof-1 | declared | parts/02-mathematical-methods/04-topology.tex:122 |