Stone–Čech Compactification
GPTKB entity
Properties (42)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Highway
Topological space |
| gptkbp:appliesTo |
Completely regular spaces
|
| gptkbp:defines |
The largest compactification of a completely regular space.
|
| gptkbp:hasRelatedPatent |
In the study of compact spaces
In the study of convergence In the study of functional spaces In the study of topological groups |
| gptkbp:hasSpecialty |
Compactness
Universal property Hausdorff_property |
| https://www.w3.org/2000/01/rdf-schema#label |
Stone–Čech Compactification
|
| gptkbp:isAccessibleBy |
Filters
Ultrafilters A completely regular space X The set of all ultrafilters on X The space βX The set of all continuous functions from X to a compact space |
| gptkbp:isCharacterizedBy |
The existence of a unique continuous extension
The extension of continuous functions The mapping of points to ultrafilters The topology generated by the open sets of X and the ultrafilters |
| gptkbp:isEquippedWith |
The compactification of non-regular spaces
The one-point compactification for locally compact spaces The Alexandroff compactification for certain spaces |
| gptkbp:isNotableFor |
Non-Hausdorff spaces
Discrete spaces Finite spaces Locally compact spaces without compactification Non-regular spaces |
| gptkbp:isRelatedTo |
Boolean algebras
The concept of convergence in topology Compact Hausdorff spaces Stone spaces The_Tychonoff_theorem |
| gptkbp:isUsedIn |
Topology
Functional analysis General topology Set-theoretic topology Algebraic_topology |
| gptkbp:namedAfter |
Jan Čech
Marek K. Stone |