Covering dimension: Difference between revisions
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{{dimension notion}} | |||
==Definition== | ==Definition== | ||
The '''topological dimension''' or '''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>. | The '''topological dimension''' or '''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>. | ||
Revision as of 22:40, 10 November 2007
Definition
The topological dimension or covering dimension of a topological space is defined as the smallest integer such that any open cover of the topological space has an open refinement that has order at most .
