Alexandroff Compactification
GPTKB entity
Properties (56)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Highway
|
| gptkbp:appliesTo |
Locally_compact_Hausdorff_spaces
|
| gptkbp:canLeadTo |
Metric spaces
Function spaces Algebraic varieties Topological groups Homogeneous spaces Non-compact topological spaces |
| gptkbp:hasRelatedPatent |
Mathematical physics
|
| gptkbp:hasSpecialty |
Unique up to homeomorphism
|
| https://www.w3.org/2000/01/rdf-schema#label |
Alexandroff Compactification
|
| gptkbp:isActiveIn |
Mathematical logic
Abstract algebra General topology |
| gptkbp:isATypeOf |
Topological space
Compactification method One-point compactification Topological construction |
| gptkbp:isCharacterizedBy |
Adding a single point
|
| gptkbp:isCompatibleWith |
Locally compact spaces
|
| gptkbp:isCounteredBy |
gptkb:Stereographic_projection
Extended real number line Projective spaces Riemann sphere |
| gptkbp:isFoundIn |
Topology theory
|
| gptkbp:isImportantFor |
Understanding limits
The study of compact spaces Algebraic_topology |
| gptkbp:isMaintainedBy |
Adding a point at infinity
|
| gptkbp:isNamedAfter |
gptkb:Pavel_Alexandroff
|
| gptkbp:isRelatedTo |
Homotopy theory
Topology of manifolds Compact subsets One-point compactification Topology of the real line Topology of the sphere Compactification_of_metric_spaces Compactification_techniques |
| gptkbp:isUsedBy |
Study convergence properties
|
| gptkbp:isUsedFor |
A method for extending spaces
A method of compactifying a space A technique for compactifying spaces. A way to add points to a space Analyze continuity |
| gptkbp:isUsedIn |
gptkb:Quantum_field_theory
Mathematical analysis Topology Graph theory Statistical mechanics Differential geometry Functional analysis Complex analysis Non-Euclidean geometry |
| gptkbp:keyFunction |
Mathematical modeling
Set theory |
| gptkbp:resultedIn |
Compact space
|