An asymmetric convex cone in a topology-free infinite-dimensional real vector space is exactly characterized by the family of step-linear functions that are positive on it and zero on its associated linear subspace.
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Infinite-dimensional Convex Cones: Internal Geometric Structure and Analytical Representation
An asymmetric convex cone in a topology-free infinite-dimensional real vector space is exactly characterized by the family of step-linear functions that are positive on it and zero on its associated linear subspace.