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:
“He that will consider the infinite power, wisdom, and goodness of the Creator of all things, will find reason to think it was not all laid out upon so inconsiderable, mean, and impotent a creature as he will find man to be; who, in all probability, is one of the lowest of all intellectual beings.”
—John Locke (1632–1704)
“Nobody of any real culture, for instance, ever talks nowadays about the beauty of sunset. Sunsets are quite old fashioned.... To admire them is a distinct sign of provincialism of temperament. Upon the other hand they go on.”
—Oscar Wilde (1854–1900)
“from above, thin squeaks of radio static,
The captured fume of space foams in our ears—”
—Hart Crane (1899–1932)