Classifying space for O(n)
In mathematics, the classifying space for the orthogonal group O may be constructed as the Grassmannian of n-planes in an infinite-dimensional real space.
Cohomology ring
The cohomology ring of with coefficients in the field of two elements is generated by the Stiefel–Whitney classes:Infinite classifying space
The canonical inclusions induce canonical inclusions on their respective classifying spaces. Their respective colimits are denoted as:is indeed the classifying space of.