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[Merged by Bors] - feat(topology/algebra/uniform_convergence): criterion for a vector subspace of Ξ± β E
to be a TVS for the topology of π-convergence
#14857
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I haven't yet looked carefully, but just a cursory glance to understand. I'll review more thoroughly later.
Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>
Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>
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The statements look ugly. I was able to improve some of them, but the ones with uniform_convergence_on
are still rough. It would be nice to figure out how to deal with it, but otherwise the PR looks good to me.
I'm okay with this as is for now. If we eventually decide that this is coming up frequently enough on bare functions and it's a pain to use then we can implement a type synonym, but that can wait for another PR. maintainer merge |
π Pull request has been placed on the maintainer queue by j-loreaux. |
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Thanks π
bors merge
β¦bspace of `Ξ± β E` to be a TVS for the topology of π-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 `π` to be nonempty and directed, but the easiest way to get that is to wait until we know that replacing `π` 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
Pull request successfully merged into master. Build succeeded: |
Ξ± β E
to be a TVS for the topology of π-convergenceΞ± β E
to be a TVS for the topology of π-convergence
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 requiringπ
to be nonempty and directed, but the easiest way to get that is to wait until we know that replacingπ
by its noncovering bornology (i.e not whatbornology
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
module_filter_basis.has_continuous_smul
when we already have a topological groupΒ #14806π
-convergenceΒ #14693