About: Cantor cube     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:Group100031264, within Data Space : dbpedia.org associated with source document(s)
QRcode icon
http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FCantor_cube

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.)

AttributesValues
rdf:type
rdfs:label
  • Cantor cube
  • Kostka Cantora
  • Cubo de Cantor
rdfs:comment
  • Kostka Cantora (ciężaru gdzie jest nieskończoną liczbą kardynalną) – przestrzeń produktowa kopii zbioru z topologią dyskretną. Kostka Cantora ciężaru oznacza jest zwykle symbolem – dokładniej: gdzie jest dowolnym zbiorem mocy oraz dla każdego zbiór jest dwuelementową przestrzenią dyskretną, np. Dla przestrzeń nazywamy zbiorem Cantora.
  • Em matemática, mas especificamente em topologia geral, o cubo de Cantor é a generalização do conjunto ternário de Cantor.
  • 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.)
foaf:isPrimaryTopicOf
dct:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
Link from a Wikipage to an external page
sameAs
dbp:wikiPageUsesTemplate
author
  • A.A. Mal'tsev
id
  • C/c023230
title
  • Colon
has 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 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.
  • Kostka Cantora (ciężaru gdzie jest nieskończoną liczbą kardynalną) – przestrzeń produktowa kopii zbioru z topologią dyskretną. Kostka Cantora ciężaru oznacza jest zwykle symbolem – dokładniej: gdzie jest dowolnym zbiorem mocy oraz dla każdego zbiór jest dwuelementową przestrzenią dyskretną, np. Dla przestrzeń nazywamy zbiorem Cantora.
  • Em matemática, mas especificamente em topologia geral, o cubo de Cantor é a generalização do conjunto ternário de Cantor.
prov:wasDerivedFrom
page length (characters) of wiki page
is foaf:primaryTopic of
is Link from a Wikipage to another Wikipage of
is Wikipage disambiguates of
Faceted Search & Find service v1.17_git51 as of Sep 16 2020


Alternative Linked Data Documents: PivotViewer | iSPARQL | ODE     Content Formats:       RDF       ODATA       Microdata      About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 08.03.3319 as of Dec 29 2020, on Linux (x86_64-centos_6-linux-glibc2.12), Single-Server Edition (61 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2021 OpenLink Software