The Lebesgue covering dimension, also called the topological dimension, of a topological space is one of several ways of defining the dimension of a space in a manner that is invariant under continuous deformation. It is defined through open covers of the space, as the smallest number n such that every open cover of the space has a refinement in which no point lies in more than n plus one of the covering sets. Because this number does not change as the space is continuously deformed, it is invariant under homeomorphisms, making it a fundamental topological property of the space.
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In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically invariant way.
Attributed To: Henri Lebesgue, Lead paragraph
In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension
In Branch: Topology, Lead paragraph
In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically invariant way.
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