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:
““. . . Me miserable! which way shall I fly
Infinite wrath and infinite despair?
Which way I fly is Hell; myself am Hell;
And, in the lowest deep, a lower deep
Still threat’ning to devour me opens wide,
To which the Hell I suffer seems a Heaven.”
—John Milton (1608–1674)
“There can be no greater error than to expect, or calculate, upon real favors from nation to nation. It is an illusion which experience must cure, which a just pride ought to discard.”
—George Washington (1732–1799)
“In the tale proper—where there is no space for development of character or for great profusion and variety of incident—mere construction is, of course, far more imperatively demanded than in the novel.”
—Edgar Allan Poe (1809–1849)