Real Projective Space - Infinite Real Projective Space

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 consciousness in each man is a sliding scale, which identifies him now with the First Cause, and now with the flesh of his body; life above life, in infinite degrees.
    Ralph Waldo Emerson (1803–1882)

    I have no connections here; only gusty collisions,
    rootless seedlings forced into bloom, that collapse.
    ...
    I am the Visiting Poet: a real unicorn,
    a wind-up plush dodo, a wax museum of the Movement.
    People want to push the buttons and see me glow.
    Marge Piercy (b. 1936)

    At first thy little being came:
    If nothing once, you nothing lose,
    For when you die you are the same;
    The space between, is but an hour,
    The frail duration of a flower.
    Philip Freneau (1752–1832)