Theorems · Theorem · general topology

AffineMap.lineMap_continuous_uncurry

∀ {R : Type u_1} {V : Type u_2} {P : Type u_3} [inst : AddCommGroup V] [inst_1 : TopologicalSpace V]
  [inst_2 : AddTorsor V P] [inst_3 : TopologicalSpace P] [IsTopologicalAddTorsor P] [inst_5 : Ring R]
  [inst_6 : Module R V] [inst_7 : TopologicalSpace R] [ContinuousSMul R V],
  Continuous fun pqt => (AffineMap.lineMap pqt.1 pqt.2.1) pqt.2.2

The line map is continuous in all arguments.

Defined in

Mathlib.Topology.Algebra.Affine

Cited by

5 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceAddTorsorTopologicalSpaceIsTopologicalAddTorsorRingModuleTopologicalSpaceContinuousSMul