 ##  [Covering Dimension](/covering-dimension) 

  ##  [Covering Dimension](https://mathlogic.quantumdictionary.io/covering-dimension-0) 

  
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**Mathematics &amp; Logic Dictionary**

 
Definition

The covering dimension (also Lebesgue covering dimension) of a topological space X is the smallest nonnegative integer n such that every open cover of X admits an open refinement whose order is at most n+1 (no point lies in more than n+1 sets); if no such n exists the dimension is infinite.