The duality between the large and small compactification radii in string theory (bosonic) is considered in the open topological membrane theory. The 2 + 1 analog of this R --> alpha'/R duality is the duality between large and small scales in the corresponding topologically massive gauge theory with the spontaneous breaking of gauge invariance. This 2 + 1 duality is a consequence of the equivalence between the Chern-Simons theory with the mass term and the topologically massive gauge theory.