Stone–Čech compactification
GPTKB entity
Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
compactification
|
| gptkbp:expansion |
continuous functions from X
|
| https://www.w3.org/2000/01/rdf-schema#label |
Stone–Čech compactification
|
| gptkbp:isA |
gptkb:Hausdorff_space
topological space topological property compactification of a space compactification technique generalization of compactification maximal compactification maximal ideal space topological construction topological extension universal property |
| gptkbp:isAccessibleBy |
a given topological space
the space X ultrafilters on X |
| gptkbp:isAssociatedWith |
the notion of convergence
|
| gptkbp:isAvenueFor |
completely regular spaces
|
| gptkbp:isCharacterizedBy |
the existence of a unique compactification
the existence of a unique continuous extension the existence of a unique extension the property of being a compact space the property of being a compactification the property of being completely regular |
| gptkbp:isConnectedTo |
the concept of limits
the concept of compactness |
| gptkbp:isNamedAfter |
Jan Čech
Marek Stone |
| gptkbp:isPartOf |
up to homeomorphism
|
| gptkbp:isRelatedTo |
general topology
ultrafilters the concept of continuity the concept of homeomorphism the concept of topology the concept of closure compact Hausdorff spaces the concept of compact subsets the concept of dense subsets the concept of separation axioms |
| gptkbp:isUsedBy |
study properties of spaces
|
| gptkbp:isUsedIn |
set theory
algebraic topology category theory mathematical analysis topology functional analysis functional spaces the study of convergence |
| gptkbp:isValuedFor |
any completely regular space
|
| gptkbp:isVisitedBy |
βX
|
| gptkbp:route |
every continuous function
|