  The local topological properties of black hole systems can be expressed by
the winding numbers as the defects. As so far, AdS black hole thermodynamics is
often depicted by the dual parameters of $(T,S),~ (P,V), (\Phi, Q)$ in the
extended phase space, while there is several study on the black hole
thermodynamics in the restricted phase space. In this paper, we analyze the
topological properties of the charged AdS black holes in the restricted phase
space under the higher dimensions and higher order curvature gravities frame.
The results show that the topological number of the charged black hole in the
same canonical ensembles is a constant and is independent of the concrete dual
thermodynamical parameters. However, the topological number in the grand
canonical ensemble is different from that in the canonical ensemble for the
same black hole system. Furthermore, these results are independent of the
dimension $d$, the highest order $k$ of the Lanczos-Lovelock densities.
