After a presentation of the context and a brief reminder of deformation
quantization, we indicate how the introduction of natural topological vector
space topologies on Hopf algebras associated with Poisson Lie groups, Lie
bialgebras and their doubles explains their dualities and provides a
comprehensive framework. Relations with deformation quantization and
applications to the deformation quantization of symmetric spaces are describedComment: 13 pages, to appear in the proceedings of the conference "Hopf
algebras in noncommutative geometry and physics" (VUB, Brussels, May 2002