diff --git a/MIL/C09_Topology/S03_Topological_Spaces.lean b/MIL/C09_Topology/S03_Topological_Spaces.lean index c4c81781..1c4241af 100644 --- a/MIL/C09_Topology/S03_Topological_Spaces.lean +++ b/MIL/C09_Topology/S03_Topological_Spaces.lean @@ -179,7 +179,7 @@ products of metric spaces. Consider for instance the type ``ℝ → ℝ``, seen a product of copies of ``ℝ`` indexed by ``ℝ``. We would like to say that pointwise convergence of sequences of functions is a respectable notion of convergence. But there is no distance on ``ℝ → ℝ`` that gives this notion of convergence. Relatedly, there is no distance ensuring that -a map ``f : X → (ℝ → ℝ)`` is continuous if and only ``fun x ↦ f x t`` is continuous for every ``t : ℝ``. +a map ``f : X → (ℝ → ℝ)`` is continuous if and only if ``fun x ↦ f x t`` is continuous for every ``t : ℝ``. We now review the data used to solve all those issues. First we can use any map ``f : X → Y`` to push or pull topologies from one side to the other. Those two operations form a Galois connection.