The Stereographic Projection in Topological Modules

The stereographic projection is constructed in topological modules. Let A be an additively symmetric closed subset of a R-module M such that 0∈int(A). If there exists continuous functional m*:M→R the dual module M*, invertible s∈U(R) and element boundary bd(A) way m*−1({s})∩int(A)=⌀, a∈m*−1({s})∩bd(A), s+m*bd(A)\{−a}⊆U(R), then following function b↦−a+2s(m*(b)+s)−1(b+a), from bd(A)\{−a} to (m*)−1({s}), well-defined (also if multiplicative inversion on R). Finally, we provide sufficient conditions for previous become homeomorphism.