  The paper introduces the notion of a locally coalgebra-Galois extension and,
as its special case, a locally cleft extension. The necessary and sufficient
conditions for a locally coalgebra-Galois extension to be a (global)
coalgebra-Galois extension are stated. As an important special case, it is
proven, that under not very restrictive conditions the gluing of two locally
cleft extensions is a globally coalgebra-Galois extension. As an example, the
quantum lens space of positive charge is constructed by gluing of two quantum
solid tori.
