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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 …
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18 votes
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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) …
algori's user avatar
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