General topology Continuous maps Concept
Proper map
Summary
A proper map is a continuous map between topological spaces under which the preimage of every compact set is compact. It is a map that does not let points "escape to infinity". Proper maps between locally compact Hausdorff spaces are closed, and they are the maps that extend continuously to one-point compactifications.
Where this leads
13 pages build on this one.
- Deformation of complex structure
- Proper holomorphic map
- Smale's degree for proper Fredholm maps
- Modification of a complex space
- Proper group action
- Cartan's coherence theorem for ideal sheaves
- Ehresmann's fibration theorem
- Thom–Mather isotopy lemmas
- Hironaka's resolution for complex spaces
- Local parametrization theorem
- Grauert's semicontinuity theorem
- Remmert's proper mapping theorem
- Grauert's direct image theorem
Further reading
About this page
| Tag | 15XEBGNGHC |
|---|---|
| URI | m2://15XEBGNGHC |
| Kind | concept |
| Writing | W0 stub |
| MSC | 54C10 |
| Specializes | Continuous map |
| Same as |
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Used by
- Deformation of complex structure
- Proper holomorphic map
- Smale's degree for proper Fredholm maps
- Modification of a complex space
- Proper group action
- Ehresmann's fibration theorem
- Thom–Mather isotopy lemmas
- Hironaka's resolution for complex spaces
- Local parametrization theorem
- Grauert's semicontinuity theorem
- Remmert's proper mapping theorem
- Grauert's direct image theorem