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- Alexandroff_extension abstract "In mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact. It is named for the Russian mathematician Pavel Alexandrov.More precisely, let X be a topological space. Then the Alexandroff extension of X is a certain compact space X* together with an open embedding c : X → X* such that the complement of X in X* consists of a single point, typically denoted ∞. The map c is a Hausdorff compactification if and only if X is a locally compact, noncompact Hausdorff space. For such spaces the Alexandroff extension is called the one-point compactification or Alexandroff compactification. The advantages of the Alexandroff compactification lie in its simple, often geometrically meaningful structure and the fact that it is in a precise sense minimal among all compactifications; the disadvantage lies in the fact that it only gives a Hausdorff compactification on the class of locally compact, noncompact Hausdorff spaces, unlike the Stone–Čech compactification which exists for any Tychonoff space, a much larger class of spaces.".
- Alexandroff_extension wikiPageExternalLink 159072.
- Alexandroff_extension wikiPageID "55611".
- Alexandroff_extension wikiPageLength "9239".
- Alexandroff_extension wikiPageOutDegree "33".
- Alexandroff_extension wikiPageRevisionID "681092412".
- Alexandroff_extension wikiPageWikiLink Addison-Wesley.
- Alexandroff_extension wikiPageWikiLink Bouquet_of_circles.
- Alexandroff_extension wikiPageWikiLink Category:Compactification.
- Alexandroff_extension wikiPageWikiLink Category:General_topology.
- Alexandroff_extension wikiPageWikiLink Compact_space.
- Alexandroff_extension wikiPageWikiLink Compactification_(mathematics).
- Alexandroff_extension wikiPageWikiLink Discrete_space.
- Alexandroff_extension wikiPageWikiLink Discrete_topology.
- Alexandroff_extension wikiPageWikiLink Embedding.
- Alexandroff_extension wikiPageWikiLink Embedding_(topology).
- Alexandroff_extension wikiPageWikiLink End_(topology).
- Alexandroff_extension wikiPageWikiLink Hausdorff_space.
- Alexandroff_extension wikiPageWikiLink Helderman_Verlag_Berlin.
- Alexandroff_extension wikiPageWikiLink Homeomorphism.
- Alexandroff_extension wikiPageWikiLink James_Munkres.
- Alexandroff_extension wikiPageWikiLink Locally_compact.
- Alexandroff_extension wikiPageWikiLink Locally_compact_space.
- Alexandroff_extension wikiPageWikiLink Mathematics.
- Alexandroff_extension wikiPageWikiLink Normal_space.
- Alexandroff_extension wikiPageWikiLink Open_and_closed_maps.
- Alexandroff_extension wikiPageWikiLink Open_mapping.
- Alexandroff_extension wikiPageWikiLink Pavel_Alexandroff.
- Alexandroff_extension wikiPageWikiLink Pavel_Alexandrov.
- Alexandroff_extension wikiPageWikiLink Pointed_set.
- Alexandroff_extension wikiPageWikiLink Polyadic_space.
- Alexandroff_extension wikiPageWikiLink Prentice_Hall.
- Alexandroff_extension wikiPageWikiLink Riemann_sphere.
- Alexandroff_extension wikiPageWikiLink Ronald_Brown_(mathematician).
- Alexandroff_extension wikiPageWikiLink Rose_(topology).
- Alexandroff_extension wikiPageWikiLink Springer-Verlag.
- Alexandroff_extension wikiPageWikiLink Springer_Science+Business_Media.
- Alexandroff_extension wikiPageWikiLink Stereographic_projection.
- Alexandroff_extension wikiPageWikiLink Stone–Čech_compactification.
- Alexandroff_extension wikiPageWikiLink Topological_space.
- Alexandroff_extension wikiPageWikiLink Topology.
- Alexandroff_extension wikiPageWikiLink Tychonoff_space.
- Alexandroff_extension wikiPageWikiLink Wallman_compactification.
- Alexandroff_extension wikiPageWikiLinkText "Alexandroff extension".
- Alexandroff_extension wikiPageWikiLinkText "one-point compactification".
- Alexandroff_extension first "V.V.".
- Alexandroff_extension hasPhotoCollection Alexandroff_extension.
- Alexandroff_extension id "A/a011260".
- Alexandroff_extension last "Fedorchuk".
- Alexandroff_extension title "Aleksandrov compactification".
- Alexandroff_extension wikiPageUsesTemplate Template:Citation.
- Alexandroff_extension wikiPageUsesTemplate Template:Harv.
- Alexandroff_extension wikiPageUsesTemplate Template:Springer.
- Alexandroff_extension subject Category:Compactification.
- Alexandroff_extension subject Category:General_topology.
- Alexandroff_extension hypernym Way.
- Alexandroff_extension comment "In mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact. It is named for the Russian mathematician Pavel Alexandrov.More precisely, let X be a topological space. Then the Alexandroff extension of X is a certain compact space X* together with an open embedding c : X → X* such that the complement of X in X* consists of a single point, typically denoted ∞.".
- Alexandroff_extension label "Alexandroff extension".
- Alexandroff_extension sameAs توسیع_الکساندرف.
- Alexandroff_extension sameAs Aleksandrovin_kompaktisointi.
- Alexandroff_extension sameAs Compactifixc3xa9_dAlexandrov.
- Alexandroff_extension sameAs Egypont-kompaktifikáció.
- Alexandroff_extension sameAs Compattificazione_di_Alexandrov.
- Alexandroff_extension sameAs 알렉산드로프_콤팩트화.
- Alexandroff_extension sameAs Compatassion_dAlexandrov.
- Alexandroff_extension sameAs m.03hfsrt.
- Alexandroff_extension sameAs Одноточкова_компактифікація.
- Alexandroff_extension sameAs Q864919.
- Alexandroff_extension sameAs Q864919.
- Alexandroff_extension wasDerivedFrom Alexandroff_extension?oldid=681092412.
- Alexandroff_extension isPrimaryTopicOf Alexandroff_extension.