mathlib3

f01de4e1 - feat(topology/algebra/uniform_convergence): criterion for a vector subspace of `α → E` to be a TVS for the topology of 𝔖-convergence (#14857)

feat(topology/algebra/uniform_convergence): criterion for a vector subspace of `α → E` to be a TVS for the topology of 𝔖-convergence (#14857) The main theorem is `uniform_convergence_on.has_continuous_smul_induced_of_image_bounded`. As explained in the module docstring, one could get rid of requiring `𝔖` to be nonempty and directed, but the easiest way to get that is to wait until we know that replacing `𝔖` by its ***noncovering*** bornology (i.e ***not*** what `bornology` currently refers to in mathlib) doesn't change the topology. This will allow to prove that strong topologies on the space of continuous linear maps between two TVSs are also TVS topologies