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15
votes
Accepted
For which classes of topological spaces Euler characteristics is defined?
The answer to the question as it is stated is that there is probably no "largest" class of spaces for which the Euler characteristic makes sense.
The answer also depends on where you would like the E …
18
votes
Accepted
Multiplicativity of Euler characteristic for non-orientable fibrations
Assume for simplicity that $B,F$ are finite CW-complexes and let $p:E\to B$ be the bundle projection.
Suppose $B$ is obtained from a CW-complex $B'$ by attaching an $n$-cell. Suppose $\chi(B')\chi(F) …