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topology.instances.real_vector_space

Continuous additive maps are -linear #

In this file we prove that a continuous map f : E →+ F between two topological vector spaces over is -linear

theorem add_monoid_hom.map_real_smul {E : Type u_1} [add_comm_group E] [module E] [topological_space E] [has_continuous_smul E] {F : Type u_2} [add_comm_group F] [module F] [topological_space F] [has_continuous_smul F] [t2_space F] (f : E →+ F) (hf : continuous f) (c : ) (x : E) :
f (c x) = c f x

A continuous additive map between two vector spaces over is -linear.

Reinterpret a continuous additive homomorphism between two real vector spaces as a continuous real-linear map.

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