  Functorial semi-norms on singular homology measure the "size" of homology
classes. A geometrically meaningful example is the $\ell^1$-semi-norm. However,
the $\ell^1$-semi-norm is not universal in the sense that it does not vanish on
as few classes as possible. We show that universal finite functorial semi-norms
do exist on singular homology on the category of topological spaces that are
homotopy equivalent to finite CW-complexes. Our arguments also apply to more
general settings of functorial semi-norms.
