Stone-Čech Compactification
GPTKB entity
Properties (47)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Highway
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| gptkbp:appliesTo |
Completely regular spaces
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| gptkbp:built |
Using ultrafilters
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| gptkbp:characteristics |
Unique up to homeomorphism
Universal property for continuous maps |
| gptkbp:currentCondition |
Every_completely_regular_space_has_a_Stone-Čech_compactification.
|
| gptkbp:defines |
The Stone-Čech compactification of a topological space is the largest compactification of that space.
|
| https://www.w3.org/2000/01/rdf-schema#label |
Stone-Čech Compactification
|
| gptkbp:isAccessibleBy |
Continuous functions from X to compact spaces
Topological space X Ultrafilters on X |
| gptkbp:isCharacterizedBy |
The compactification being a compactification of a perfect space.
The compactification being extremally disconnected. The compactification being a completely regular space. The compactification being a limit point compact. The compactification being a perfect space. The compactification being maximal. The compactification being unique. The compactification being universal. The existence of a unique continuous extension. The extension of continuous functions. The existence of a dense embedding into a compact space. The compactification being a zero-dimensional space. The compactification being a compactification of a completely regular space. The compactification being a compactification of a zero-dimensional space. The_compactification_being_a_compactification_of_a_compact_Hausdorff_space. The_compactification_being_Hausdorff. The_compactification_being_a_Tychonoff_space. The_compactification_being_a_compact_Hausdorff_space. The_compactification_being_a_compactification_of_a_Tychonoff_space. |
| gptkbp:isPartOf |
Up to homeomorphism.
|
| gptkbp:isRelatedTo |
Category theory
Filters Set theory Boolean algebras Ultrafilters Stone spaces Compactification_techniques |
| gptkbp:isUsedIn |
Topology
Functional analysis |
| gptkbp:namedAfter |
Jan Čech
Marek K. Stone |
| gptkbp:relatedTo |
Topological spaces
Continuous functions Homeomorphisms Compact spaces |
| gptkbp:symbolizes |
βX
|