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- Cantor_cube abstract "In mathematics, a Cantor cube is a topological group of the form {0, 1}A for some index set A. Its algebraic and topological structures are the group direct product and product topology over the cyclic group of order 2 (which is itself given the discrete topology).If A is a countably infinite set, the corresponding Cantor cube is a Cantor space. Cantor cubes are special among compact groups because every compact group is a continuous image of one, although usually not a homomorphic image. (The literature can be unclear, so for safety, assume all spaces are Hausdorff.)Topologically, any Cantor cube is:homogeneous;compact;zero-dimensional;AE(0), an absolute extensor for compact zero-dimensional spaces. (Every map from a closed subset of such a space into a Cantor cube extends to the whole space.)By a theorem of Schepin, these four properties characterize Cantor cubes; any space satisfying the properties is homeomorphic to a Cantor cube.In fact, every AE(0) space is the continuous image of a Cantor cube, and with some effort one can prove that every compact group is AE(0). It follows that every zero-dimensional compact group is homeomorphic to a Cantor cube, and every compact group is a continuous image of a Cantor cube.".
- Cantor_cube wikiPageID "4999981".
- Cantor_cube wikiPageRevisionID "544368634".
- Cantor_cube author "A.A. Mal'tsev".
- Cantor_cube hasPhotoCollection Cantor_cube.
- Cantor_cube id "C/c023230".
- Cantor_cube title "Colon".
- Cantor_cube subject Category:Topological_groups.
- Cantor_cube type Abstraction100002137.
- Cantor_cube type Group100031264.
- Cantor_cube type TopologicalGroups.
- Cantor_cube comment "In mathematics, a Cantor cube is a topological group of the form {0, 1}A for some index set A. Its algebraic and topological structures are the group direct product and product topology over the cyclic group of order 2 (which is itself given the discrete topology).If A is a countably infinite set, the corresponding Cantor cube is a Cantor space. Cantor cubes are special among compact groups because every compact group is a continuous image of one, although usually not a homomorphic image.".
- Cantor_cube label "Cantor cube".
- Cantor_cube label "Cubo de Cantor".
- Cantor_cube label "Kostka Cantora".
- Cantor_cube sameAs Kostka_Cantora.
- Cantor_cube sameAs Cubo_de_Cantor.
- Cantor_cube sameAs m.0cz6_t.
- Cantor_cube sameAs Q5034034.
- Cantor_cube sameAs Q5034034.
- Cantor_cube sameAs Cantor_cube.
- Cantor_cube wasDerivedFrom Cantor_cube?oldid=544368634.
- Cantor_cube isPrimaryTopicOf Cantor_cube.