The Stereographic Projection in Topological Modules

Abstract

The stereographic projection is constructed in topological modules. Let A be an additively symmetric closed subset of a topological R-module M such that (Formula presented.). If there exists a continuous functional (Formula presented.) in the dual module (Formula presented.), an invertible (Formula presented.) and an element a in the topological boundary (Formula presented.) of A in such a way that (Formula presented.), (Formula presented.), and (Formula presented.), then the following function (Formula presented.), from (Formula presented.) to (Formula presented.), is a well-defined stereographic projection (also continuous if multiplicative inversion is continuous on R). Finally, we provide sufficient conditions for the previous stereographic projection to become a homeomorphism