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