Lebesgue covering dimension

In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is defined to be the minimum value of n, such that every open cover has a refinement in which no point is included in more than n+1 elements. If no such minimal n exists, the space is said to be infinite dimensional. In this context, a refinement is a second open cover such that every set of the second open cover is a subset of some set in the first open cover. It is named after Henri Lebesgue, although it was independently arrived at by a number of contemporaneous mathematicians.
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