Topological dimension: Difference between revisions

Latest revision as of 12:20, 8 June 2008

Topological dimension: The topological dimension or covering dimension or Lebesgue covering dimension of a topological space is defined as the smallest integer $m$ such that any open cover of the topological space has an open refinement that has order at most $m + 1$ .

Primary subject wiki entry: Topospaces:Topological dimension

Also located at: Wikipedia:Lebesgue covering dimension

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 <noinclude>[[Status::Standard non-basic definition| ]][[Topic::Point-set topology| ]][[Primary wiki::Topospaces| ]]</noinclude>
-''Topological dimension''': The '''topological dimension''' or '''covering dimension''' or '''Lebesgue covering dimension''' of a [[topological space]] is defined as the smallest integer <math>m</math> such that any [[open cover]] of the topological space has an open [[refinement]] that has [[order of a collection of subsets|order]] at most <math>m + 1</math>.
+'''Topological dimension''': The '''topological dimension''' or '''covering dimension''' or '''Lebesgue covering dimension''' of a [[topological space]] is defined as the smallest integer <math>m</math> such that any [[open cover]] of the topological space has an open [[refinement]] that has [[order of a collection of subsets|order]] at most <math>m + 1</math>.
 Primary subject wiki entry: [[Topospaces:Topological dimension]]
 Also located at: [[Wikipedia:Lebesgue covering dimension]]