Abstract: In the consubstantial N-dimensional pure spaces, the mapping relations in the pairwise
adjacent domains can be built through the one-to-one projective transformation. Through the simulated
experiment of the adjacent domain in computers as well as the strict proof, it is found and proved that,
in the N-dimensional pure spaces, the maxima of pairwise adjacent domains in the N-1 (N minus 1)
dimension is N+1 (N plus 1). In the configuration diagram of each N-1 dimension, there are at most
N+1 kinds of dyeing. The building of the visible three-dimensional spherical models for "the Solid
Geometry" can provide a visible "Standard Cosmic Projection Model" for the modern science.

Key words: the pure space, projective transformation, mapping analysis, the N-dimensional adjacent
domains, N+1 dyeing theorem