# All Science Fair Projects

## Science Fair Project Encyclopedia for Schools!

 Search    Browse    Forum  Coach    Links    Editor    Help    Tell-a-Friend    Encyclopedia    Dictionary

# Science Fair Project Encyclopedia

For information on any area of science that interests you,
enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.).
Or else, you can start by choosing any of the categories below.

# Lebesgue covering dimension

(Redirected from Topological 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 any open cover has a refinement with no point included in more than n+1 elements.

Here a refinement is a second open cover, of open sets selected from the given open cover. To illustrate the concept, consider open covers of the unit circle, by open arcs. The circle has dimension 1, by this definition, because any such cover can be refined to the stage where a given point x of the circle is contained in at most 2 arcs. That is, whatever arcs we begin with, enough can be discarded so that there are just simple overlaps.

The Lebesgue covering dimension gives the correct answer for the dimension of a finite simplicial complex; this is the Lebesgue covering theorem.