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:
“One who pressed forward incessantly and never rested from his labors, who grew fast and made infinite demands on life, would always find himself in a new country or wilderness, and surrounded by the raw material of life. He would be climbing over the prostrate stems of primitive forest-trees.”
—Henry David Thoreau (1817–1862)
“Talking about dreams is like talking about movies, since the cinema uses the language of dreams; years can pass in a second and you can hop from one place to another. It’s a language made of image. And in the real cinema, every object and every light means something, as in a dream.”
—Frederico Fellini (1920–1993)
“True spoiling is nothing to do with what a child owns or with amount of attention he gets. he can have the major part of your income, living space and attention and not be spoiled, or he can have very little and be spoiled. It is not what he gets that is at issue. It is how and why he gets it. Spoiling is to do with the family balance of power.”
—Penelope Leach (20th century)