  We show that pseudovarieties of finitely generated algebras, i.e., classes
$C$ of finitely generated algebras closed under finite products, homomorphic
images, and subalgebras, can be described via a uniform structure $U$ on the
free algebra for $C$: the members of $C$ then are precisely those finitely
generated algebras $A$ for which the natural mapping from the free algebra onto
the term clone of $A$ is well-defined and uniformly continuous with respect to
the uniformity $U$ and the uniformity of pointwise convergence on the term
clone of $A$, respectively. Our result unifies earlier theorems describing
pseudovarieties of finite algebras and the pseudovariety generated by a single
oligomorphic algebra.
