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- Alexandrov_topology abstract "In topology, an Alexandrov space (or Alexandrov-discrete space) is a topological space in which the intersection of any family of open sets is open. It is an axiom of topology that the intersection of any finite family of open sets is open. In an Alexandrov space the finite restriction is dropped.Alexandrov topologies are uniquely determined by their specialization preorders. Indeed, given any preorder ≤ on a set X, there is a unique Alexandrov topology on X for which the specialization preorder is ≤. The open sets are just the upper sets with respect to ≤. Thus, Alexandrov topologies on X are in one-to-one correspondence with preorders on X.Alexandrov spaces are also called finitely generated spaces since their topology is uniquely determined by the family of all finite subspaces. Alexandrov spaces can be viewed as a generalization of finite topological spaces.".
- Alexandrov_topology wikiPageID "542198".
- Alexandrov_topology wikiPageRevisionID "592935660".
- Alexandrov_topology hasPhotoCollection Alexandrov_topology.
- Alexandrov_topology subject Category:Closure_operators.
- Alexandrov_topology subject Category:Order_theory.
- Alexandrov_topology subject Category:Properties_of_topological_spaces.
- Alexandrov_topology type Abstraction100002137.
- Alexandrov_topology type ClosureOperators.
- Alexandrov_topology type Function113783816.
- Alexandrov_topology type MathematicalRelation113783581.
- Alexandrov_topology type Operator113786413.
- Alexandrov_topology type Possession100032613.
- Alexandrov_topology type PropertiesOfTopologicalSpaces.
- Alexandrov_topology type Property113244109.
- Alexandrov_topology type Relation100031921.
- Alexandrov_topology comment "In topology, an Alexandrov space (or Alexandrov-discrete space) is a topological space in which the intersection of any family of open sets is open. It is an axiom of topology that the intersection of any finite family of open sets is open. In an Alexandrov space the finite restriction is dropped.Alexandrov topologies are uniquely determined by their specialization preorders.".
- Alexandrov_topology label "Alexandrov topology".
- Alexandrov_topology label "Przestrzeń Aleksandrowa".
- Alexandrov_topology label "Topologia de Alexandrov".
- Alexandrov_topology label "Topologie d'Alexandroff".
- Alexandrov_topology label "Topología de Alexandrov".
- Alexandrov_topology sameAs Topología_de_Alexandrov.
- Alexandrov_topology sameAs Topologie_d'Alexandroff.
- Alexandrov_topology sameAs Przestrzeń_Aleksandrowa.
- Alexandrov_topology sameAs Topologia_de_Alexandrov.
- Alexandrov_topology sameAs m.02n998.
- Alexandrov_topology sameAs Q3532117.
- Alexandrov_topology sameAs Q3532117.
- Alexandrov_topology sameAs Alexandrov_topology.
- Alexandrov_topology wasDerivedFrom Alexandrov_topology?oldid=592935660.
- Alexandrov_topology isPrimaryTopicOf Alexandrov_topology.