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:
“The nonchalance and dolce-far-niente air of nature and society hint at infinite periods in the progress of mankind.”
—Henry David Thoreau (1817–1862)
“Miss C_____ is ... remarkably neat in her person and is uncommonly diligent in every part of useful economy.... She hath indeed under her father’s tuition acquired ... a large share of real learning of almost all the living and dead languages. Nor was the leisure which she found for such acquirements produced by neglecting anything necessary or useful for the family, but by the most assiduous industry.”
—Sarah Fielding (1710–1768)
“The flattering, if arbitrary, label, First Lady of the Theatre, takes its toll. The demands are great, not only in energy but eventually in dramatic focus. It is difficult, if not impossible, for a star to occupy an inch of space without bursting seams, cramping everyone else’s style and unbalancing a play. No matter how self-effacing a famous player may be, he makes an entrance as a casual neighbor and the audience interest shifts to the house next door.”
—Helen Hayes (1900–1993)