  We extend the definition of quasi-finite complexes by considering not
necessarily countable complexes. We provide a characterization of quasi-finite
complexes in terms of L-invertible maps and dimensional properties of
compactifications. Several results related to the class of quasi-finite
complexes are established, such as completion of metrizable spaces, existence
of universal spaces and a version of the factorization theorem. Further, we
extend the definition of UV(L)-spaces on non-compact case and show that some
properties of UV(n)-spaces and UV(n)-maps remain valid, respectively, for
UV(L)-spaces and UV(L)-maps.
