Infinite Real Projective Space
The infinite real projective space is constructed as the direct limit or union of the finite projective spaces:
Topologically, this space is double-covered by the infinite sphere, which is contractible. The infinite projective space is therefore the Eilenberg-MacLane space and it is BO(1), the classifying space for line bundles. More generally, the infinite Grassmannians are the classifying spaces for finite rank vector bundles.
Its cohomology ring modulo 2 is
where is the first Stiefel–Whitney class: it is the free -algebra on, which has degree 1.
Read more about this topic: Real Projective Space
Famous quotes containing the words infinite, real and/or space:
“Henry B. Adams was the first in an infinite series to discover and admit to himself that he really did not care whether truth was, or was not, true. He did not even care that it should be proved true, unless the process were new and amusing. He was a Darwinian for fun.”
—Henry Brooks Adams (1838–1918)
“There is no real teacher who in practise does not believe in the existence of the soul, or in a magic that acts on it through speech.”
—Allan Bloom (1930–1992)
“Finally she grew quiet, and after that, coherent thought. With this, stalked through her a cold, bloody rage. Hours of this, a period of introspection, a space of retrospection, then a mixture of both. Out of this an awful calm.”
—Zora Neale Hurston (1891–1960)