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The separation of two sets (or more specific of two cones) plays an importantrole in different fields of mathematics such as variational analysis, convexanalysis, convex geometry, optimization. In the paper, we derive some newresults for the separation of two not necessarily convex cones by a (convex)cone / conical surface in real (topological) linear spaces. Basically, wefollow the separation approach by Kasimbeyli (2010, SIAM J. Optim. 20) based onaugmented dual cones and Bishop-Phelps type (normlinear) separating functions.Classical separation theorems for convex sets are the key tool for proving ourmain nonlinear cone separation theorems.

Nonlinear Cone Separation Theorems in Real Topological Linear Spaces