In our previous paper (S. Nakamura, T. Konishi and A. Kitada: J. Phys.
Sec. Jpn. 64 (1995) 731), we topologized a polycrystal by labeling th
e axes of each single crystal within the polycrystal. In this paper, w
e propose another topologization of polycrystal which is independent o
f the labeling of the axes, and the order of the vectors in the base.
This natural topologization still conserves the completeness of the po
lycrystal and, therefore, the existence within it of a compact set wit
h self-similarity is still guaranteed.