= Bockstein on infinite real projective space
{c}
{title2=$\beta(u_n)=(n\bmod2)u_{n+1}$}
For the coefficient sequence $0\to\mathbb Z_2\to\mathbb Z_4\to\mathbb Z_2\to0$, the <Bockstein homomorphism> on <infinite-dimensional real projective space> is zero from an even degree and an isomorphism from an odd degree. In <cellular cohomology>, lift the mod-two generator to $1\in\mathbb Z_4$. The coboundary is zero in even degree and two in odd degree; identifying two with the image of $1\in\mathbb Z_2$ gives the formula.
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